To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
We can solve this by setting the two equations equal to each other:
2x + 7 = -3x + 2
Now, let's solve for x:
2x + 3x = 2 - 7
5x = -5
x = -1
Now, substitute the value of x into either of the original equations to find y:
y = 2(-1) + 7
y = -2 + 7
y = 5
Therefore, the solution to this system of equations is x = -1 and y = 5.
y=2x+7
y=-3x+2
what is the solution to this
34 answers
At a local fitness center, members pay $8 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Thus, for
aerobics classes, the cost will be the same for members and nonmembers.
(Type a whole number.)
Thus, for
aerobics classes, the cost will be the same for members and nonmembers.
(Type a whole number.)
Let's denote the number of aerobics classes as "x."
For members, the cost is $8 (membership fee) + $3 (cost per aerobics class) * x (number of aerobics classes).
For nonmembers, the cost is $4 (cost per aerobics class) * x (number of aerobics classes).
We can set up the equation:
8 + 3x = 4x
Subtracting 3x from both sides:
8 = x
Therefore, the cost will be the same for members and nonmembers when the number of aerobics classes is 8.
For members, the cost is $8 (membership fee) + $3 (cost per aerobics class) * x (number of aerobics classes).
For nonmembers, the cost is $4 (cost per aerobics class) * x (number of aerobics classes).
We can set up the equation:
8 + 3x = 4x
Subtracting 3x from both sides:
8 = x
Therefore, the cost will be the same for members and nonmembers when the number of aerobics classes is 8.
y-2x=2
3y=6x+6
the solution of the system is
3y=6x+6
the solution of the system is
To find the solution to this system of equations, we can use either substitution or elimination method. Here, we will use the elimination method to solve the system of equations.
First, let's multiply the first equation by 3 to make the coefficients of y the same:
3(y - 2x) = 3(2)
This simplifies to:
3y - 6x = 6
Now, we have the following two equations:
3y = 6x + 6
3y - 6x = 6
We can subtract the second equation from the first equation:
(3y - 6x) - (3y - 6x) = (6x + 6) - 6
Simplifying, we get:
0 = 0
The equation 0 = 0 is a true statement. This means that the two original equations are dependent and consistent, meaning they represent the same line. Therefore, there are infinitely many solutions to this system of equations.
Geometrically, this means that the two lines represented by the equations are coincident, resulting in an infinite number of points of intersection.
In summary, the solution to this system of equations is an infinite number of ordered pairs (x, y) that satisfy both equations.
First, let's multiply the first equation by 3 to make the coefficients of y the same:
3(y - 2x) = 3(2)
This simplifies to:
3y - 6x = 6
Now, we have the following two equations:
3y = 6x + 6
3y - 6x = 6
We can subtract the second equation from the first equation:
(3y - 6x) - (3y - 6x) = (6x + 6) - 6
Simplifying, we get:
0 = 0
The equation 0 = 0 is a true statement. This means that the two original equations are dependent and consistent, meaning they represent the same line. Therefore, there are infinitely many solutions to this system of equations.
Geometrically, this means that the two lines represented by the equations are coincident, resulting in an infinite number of points of intersection.
In summary, the solution to this system of equations is an infinite number of ordered pairs (x, y) that satisfy both equations.
A cell phone provider offers a plan that costs $40 per month plus $0.20 per text message sent or received. A comparable plan costs $70 per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each month?
In order for the plans to cost the same,
text messages would have to be sent or received.
(Simplify your answer. Type an integer or a decimal.)
a. How many text messages would have to be sent or received in order for the plans to cost the same each month?
In order for the plans to cost the same,
text messages would have to be sent or received.
(Simplify your answer. Type an integer or a decimal.)
Let's denote the number of text messages as "x."
For the first plan, the cost is $40 (monthly fee) + $0.20 (cost per text message) * x (number of text messages).
For the second plan, the cost is $70 (monthly fee) regardless of the number of text messages.
We can set up the equation:
40 + 0.20x = 70
Now, let's solve for x:
0.20x = 70 - 40
0.20x = 30
x = 30 / 0.20
x = 150
Therefore, in order for the plans to cost the same each month, 150 text messages would have to be sent or received.
For the first plan, the cost is $40 (monthly fee) + $0.20 (cost per text message) * x (number of text messages).
For the second plan, the cost is $70 (monthly fee) regardless of the number of text messages.
We can set up the equation:
40 + 0.20x = 70
Now, let's solve for x:
0.20x = 70 - 40
0.20x = 30
x = 30 / 0.20
x = 150
Therefore, in order for the plans to cost the same each month, 150 text messages would have to be sent or received.
y=-3x+27
6y-x+9=0
the solution is
6y-x+9=0
the solution is
To find the solution to this system of equations, we can use the substitution or elimination method. Here, we will use the substitution method to solve the system.
Let's start by solving the first equation for y:
y = -3x + 27
Now, substitute this expression for y into the second equation:
6(-3x + 27) - x + 9 = 0
Simplify the equation:
-18x + 162 - x + 9 = 0
Combine like terms:
-19x + 171 = 0
Subtract 171 from both sides:
-19x = -171
Divide both sides by -19:
x = -171 / -19
x = 9
Now, substitute this value of x back into the first equation to find y:
y = -3(9) + 27
y = -27 + 27
y = 0
Therefore, the solution to this system of equations is x = 9 and y = 0.
Let's start by solving the first equation for y:
y = -3x + 27
Now, substitute this expression for y into the second equation:
6(-3x + 27) - x + 9 = 0
Simplify the equation:
-18x + 162 - x + 9 = 0
Combine like terms:
-19x + 171 = 0
Subtract 171 from both sides:
-19x = -171
Divide both sides by -19:
x = -171 / -19
x = 9
Now, substitute this value of x back into the first equation to find y:
y = -3(9) + 27
y = -27 + 27
y = 0
Therefore, the solution to this system of equations is x = 9 and y = 0.
2x+5y=21
-5x+y=15
What is the solution of the system?
-5x+y=15
What is the solution of the system?
To find the solution to this system of equations, we can use the method of substitution or elimination. Here, let's use the elimination method.
We can multiply the second equation by 5 to make the coefficients of y the same:
-5x + y = 15
(5)(-5x + y) = (5)(15)
-25x + 5y = 75
Now, we have the following two equations:
2x + 5y = 21
-25x + 5y = 75
We can subtract the first equation from the second equation:
(-25x + 5y) - (2x + 5y) = 75 - 21
Simplifying, we get:
-27x = 54
Divide both sides by -27:
x = -2
Now, substitute this value of x into the first equation to find y:
2(-2) + 5y = 21
-4 + 5y = 21
5y = 25
y = 5
Therefore, the solution to this system of equations is x = -2 and y = 5.
We can multiply the second equation by 5 to make the coefficients of y the same:
-5x + y = 15
(5)(-5x + y) = (5)(15)
-25x + 5y = 75
Now, we have the following two equations:
2x + 5y = 21
-25x + 5y = 75
We can subtract the first equation from the second equation:
(-25x + 5y) - (2x + 5y) = 75 - 21
Simplifying, we get:
-27x = 54
Divide both sides by -27:
x = -2
Now, substitute this value of x into the first equation to find y:
2(-2) + 5y = 21
-4 + 5y = 21
5y = 25
y = 5
Therefore, the solution to this system of equations is x = -2 and y = 5.
Tell whether the system has one solution, infinitely many solutions, or no solution.
25y=-17.5x+45
3.5x+5y=9
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
25y=-17.5x+45
3.5x+5y=9
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
To determine the solution to this system of equations, we can use the method of substitution or elimination. Here, let's use the elimination method.
First, let's multiply the first equation by 2 to make the coefficients of x the same:
50y = -35x + 90
Now, we have the following two equations:
50y = -35x + 90
3.5x + 5y = 9
Now, we can multiply the second equation by 10 to make the coefficients of y the same:
35x + 50y = 90
Now the system of equations is:
50y = -35x + 90
35x + 50y = 90
When we compare the two equations, we see that they are the same except that one equation is multiplied entirely by -1. This means that the two equations represent the same line.
Therefore, the system of equations has infinitely many solutions since any point on the line represented by the first equation will also satisfy the second equation.
Therefore, the correct answer is:
A. The system has infinitely many solutions.
First, let's multiply the first equation by 2 to make the coefficients of x the same:
50y = -35x + 90
Now, we have the following two equations:
50y = -35x + 90
3.5x + 5y = 9
Now, we can multiply the second equation by 10 to make the coefficients of y the same:
35x + 50y = 90
Now the system of equations is:
50y = -35x + 90
35x + 50y = 90
When we compare the two equations, we see that they are the same except that one equation is multiplied entirely by -1. This means that the two equations represent the same line.
Therefore, the system of equations has infinitely many solutions since any point on the line represented by the first equation will also satisfy the second equation.
Therefore, the correct answer is:
A. The system has infinitely many solutions.
Tell whether the system has one solution, infinitely many solutions, or no solution.
18=8y+13x
13x+8y=19
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
18=8y+13x
13x+8y=19
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
To determine the solution to this system of equations, we can use the method of substitution or elimination. Here, let's use the elimination method.
The two equations presented are:
18 = 8y + 13x
13x + 8y = 19
When we compare the two equations, we can see that their coefficients are the same and their constant terms are different.
This means that the two lines represented by the equations are parallel and will never intersect, indicating that the system has no solution.
Therefore, the correct answer is:
C. The system has no solution.
The two equations presented are:
18 = 8y + 13x
13x + 8y = 19
When we compare the two equations, we can see that their coefficients are the same and their constant terms are different.
This means that the two lines represented by the equations are parallel and will never intersect, indicating that the system has no solution.
Therefore, the correct answer is:
C. The system has no solution.
Your school's talent show will feature 12 solo acts and 3 ensemble acts. The show will last 117 minutes. The 6 solo performers judged best will give a repeat performance at a second 75 minute show, which will also feature the 3 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b).
a) Write a system of equations to model the situation.
A.12x plus 3 y equals 75 6 x plus 3 y equals 117
B.3 x plus 12 y equals 117 3 x plus 6 y equals 75
C.12 x plus 3 y equals 117 6 x plus 3 y equals 75
D.3 x plus 12 y equals 75 3 x plus 6 y equals 117
a) Write a system of equations to model the situation.
A.12x plus 3 y equals 75 6 x plus 3 y equals 117
B.3 x plus 12 y equals 117 3 x plus 6 y equals 75
C.12 x plus 3 y equals 117 6 x plus 3 y equals 75
D.3 x plus 12 y equals 75 3 x plus 6 y equals 117
To write a system of equations that models the given situation, we need to consider the number of solo acts, ensemble acts, and the total duration of the show.
Let x represent the duration of each solo act in minutes, and y represent the duration of each ensemble act in minutes.
We know that there are 12 solo acts performing and their total duration should be 75 minutes. Thus, the equation can be written as:
12x + 3y = 75
Likewise, we know that there are 3 ensemble acts and their total duration should be 117 minutes. We also know that the 6 solo acts chosen for the second show will perform again. Therefore, their total duration should be 75 minutes. So, the equation can be written as:
6x + 3y = 117
Hence, the correct choice for the system of equations is:
A. 12x + 3y = 75
6x + 3y = 117
Let x represent the duration of each solo act in minutes, and y represent the duration of each ensemble act in minutes.
We know that there are 12 solo acts performing and their total duration should be 75 minutes. Thus, the equation can be written as:
12x + 3y = 75
Likewise, we know that there are 3 ensemble acts and their total duration should be 117 minutes. We also know that the 6 solo acts chosen for the second show will perform again. Therefore, their total duration should be 75 minutes. So, the equation can be written as:
6x + 3y = 117
Hence, the correct choice for the system of equations is:
A. 12x + 3y = 75
6x + 3y = 117
thats wrong
Apologies for the incorrect response. Let's reconsider the system of equations based on the given information.
We have:
12 solo acts, each lasting x minutes.
3 ensemble acts, each lasting y minutes.
The total duration of the talent show is 117 minutes. Thus, we can set up the equation:
12x + 3y = 117
For the second show, only the 6 solo acts judged best will perform again, and the total duration will be 75 minutes. So, we can set up the equation:
6x + 3y = 75
Therefore, the correct choice for the system of equations is:
C. 12x + 3y = 117
6x + 3y = 75
We have:
12 solo acts, each lasting x minutes.
3 ensemble acts, each lasting y minutes.
The total duration of the talent show is 117 minutes. Thus, we can set up the equation:
12x + 3y = 117
For the second show, only the 6 solo acts judged best will perform again, and the total duration will be 75 minutes. So, we can set up the equation:
6x + 3y = 75
Therefore, the correct choice for the system of equations is:
C. 12x + 3y = 117
6x + 3y = 75
Solve the system from part (a).
To solve the system of equations:
12x + 3y = 117
6x + 3y = 75
We can use the elimination method.
First, let's multiply the second equation by -2 to make the coefficients of x the same:
-2(6x + 3y) = -2(75)
-12x - 6y = -150
Now, we have the following two equations:
12x + 3y = 117
-12x - 6y = -150
Adding the two equations together, we can eliminate the x terms:
(12x + 3y) + (-12x - 6y) = 117 + (-150)
Simplifying, we get:
-3y = -33
Divide both sides by -3:
y = 11
Now, substitute this value of y into one of the original equations to find x. Let's substitute it into the first equation:
12x + 3(11) = 117
12x + 33 = 117
12x = 84
x = 7
Therefore, the solution to this system of equations is x = 7 and y = 11.
12x + 3y = 117
6x + 3y = 75
We can use the elimination method.
First, let's multiply the second equation by -2 to make the coefficients of x the same:
-2(6x + 3y) = -2(75)
-12x - 6y = -150
Now, we have the following two equations:
12x + 3y = 117
-12x - 6y = -150
Adding the two equations together, we can eliminate the x terms:
(12x + 3y) + (-12x - 6y) = 117 + (-150)
Simplifying, we get:
-3y = -33
Divide both sides by -3:
y = 11
Now, substitute this value of y into one of the original equations to find x. Let's substitute it into the first equation:
12x + 3(11) = 117
12x + 33 = 117
12x = 84
x = 7
Therefore, the solution to this system of equations is x = 7 and y = 11.
How long is each solo act?
To find the duration of each solo act, we can substitute the values of x and y into one of the equations from the system.
Let's use the first equation:
12x + 3y = 117
Substituting x = 7 and y = 11:
12(7) + 3(11) = 117
84 + 33 = 117
117 = 117
The equation is true, so the values of x = 7 and y = 11 are a valid solution.
Therefore, each solo act lasts for 7 minutes.
Let's use the first equation:
12x + 3y = 117
Substituting x = 7 and y = 11:
12(7) + 3(11) = 117
84 + 33 = 117
117 = 117
The equation is true, so the values of x = 7 and y = 11 are a valid solution.
Therefore, each solo act lasts for 7 minutes.
How long is each ensemble act?
To determine the duration of each ensemble act, we can substitute the values of x and y into one of the equations from the system.
Using the second equation:
6x + 3y = 75
Substituting x = 7:
6(7) + 3y = 75
42 + 3y = 75
Subtracting 42 from both sides:
3y = 75 - 42
3y = 33
Dividing both sides by 3:
y = 11
The equation is true, so the values of x = 7 and y = 11 are a valid solution.
Therefore, each ensemble act lasts for 11 minutes.
Using the second equation:
6x + 3y = 75
Substituting x = 7:
6(7) + 3y = 75
42 + 3y = 75
Subtracting 42 from both sides:
3y = 75 - 42
3y = 33
Dividing both sides by 3:
y = 11
The equation is true, so the values of x = 7 and y = 11 are a valid solution.
Therefore, each ensemble act lasts for 11 minutes.
Solve the system using elimination.
2x-5y=-21
5x+2y=-9
The solution is
(Simplify your answer. Type an ordered pair.)
2x-5y=-21
5x+2y=-9
The solution is
(Simplify your answer. Type an ordered pair.)
To solve the system of equations using elimination, we'll multiply the first equation by 5, and the second equation by 2 to make the coefficients of either x or y the same.
5(2x - 5y) = 5(-21)
2(5x + 2y) = 2(-9)
This simplifies to:
10x - 25y = -105
10x + 4y = -18
Next, we'll subtract the second equation from the first equation:
(10x - 25y) - (10x + 4y) = -105 - (-18)
Simplifying, we have:
-29y = -87
Dividing both sides by -29, we get:
y = 3
Now substitute the value of y back into one of the original equations, let's use the first equation:
2x - 5(3) = -21
Simplifying:
2x - 15 = -21
Adding 15 to both sides:
2x = -6
Dividing both sides by 2:
x = -3
Hence, the solution to the system of equations is (x, y) = (-3, 3).
5(2x - 5y) = 5(-21)
2(5x + 2y) = 2(-9)
This simplifies to:
10x - 25y = -105
10x + 4y = -18
Next, we'll subtract the second equation from the first equation:
(10x - 25y) - (10x + 4y) = -105 - (-18)
Simplifying, we have:
-29y = -87
Dividing both sides by -29, we get:
y = 3
Now substitute the value of y back into one of the original equations, let's use the first equation:
2x - 5(3) = -21
Simplifying:
2x - 15 = -21
Adding 15 to both sides:
2x = -6
Dividing both sides by 2:
x = -3
Hence, the solution to the system of equations is (x, y) = (-3, 3).
Tell whether the system has one solution, infinitely many solutions, or no solution.
-x+6y=-1
3x-18y=3
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
-x+6y=-1
3x-18y=3
Choose the correct answer below.
A.
The system has infinitely many solutions.
B.
The system has one solution.
C.
The system has no solution.
To determine the solution to the system of equations, we can use the elimination method or substitution method. Here, let's use the elimination method.
Multiplying the first equation by 3, and the second equation by -1, we get:
-3x + 18y = -3
-(-3x + 18y) = -3
This simplifies to:
-3x + 18y = -3
3x - 18y = -3
Adding the two equations together, we can eliminate the y terms:
(-3x + 18y) + (3x - 18y) = -3 + (-3)
Simplifying, we get:
0 = -6
The equation 0 = -6 is false, which means that the two original equations are inconsistent and cannot be satisfied simultaneously. Therefore, the system has no solution.
Hence, the correct answer is:
C. The system has no solution.
Multiplying the first equation by 3, and the second equation by -1, we get:
-3x + 18y = -3
-(-3x + 18y) = -3
This simplifies to:
-3x + 18y = -3
3x - 18y = -3
Adding the two equations together, we can eliminate the y terms:
(-3x + 18y) + (3x - 18y) = -3 + (-3)
Simplifying, we get:
0 = -6
The equation 0 = -6 is false, which means that the two original equations are inconsistent and cannot be satisfied simultaneously. Therefore, the system has no solution.
Hence, the correct answer is:
C. The system has no solution.
Solve the system using any method.
x+y=0.8
4x+y=0.2
What is the solution of the system of equations? Select the correct choice and fill in any answer boxes in your choice below.
A.
enter your response here
(Simplify your answer. Type an ordered pair. Type an integer or a decimal.)
B.
There are infinitely many solutions.
C.
There is no solution.
x+y=0.8
4x+y=0.2
What is the solution of the system of equations? Select the correct choice and fill in any answer boxes in your choice below.
A.
enter your response here
(Simplify your answer. Type an ordered pair. Type an integer or a decimal.)
B.
There are infinitely many solutions.
C.
There is no solution.
To solve the system of equations, we can use the method of substitution or elimination. Here, let's use the elimination method.
We have the following system of equations:
x + y = 0.8
4x + y = 0.2
To eliminate the y term, let's multiply the first equation by -1:
-1(x + y) = -1(0.8)
-x - y = -0.8
Now, we have:
-x - y = -0.8
4x + y = 0.2
Adding the two equations together, we can eliminate the y term:
(-x - y) + (4x + y) = -0.8 + 0.2
Simplifying, we get:
3x = -0.6
Dividing both sides by 3:
x = -0.2
Now, substitute the value of x back into one of the original equations, let's use the second equation:
4(-0.2) + y = 0.2
-0.8 + y = 0.2
y = 1
Therefore, the solution to this system of equations is (x, y) = (-0.2, 1).
Therefore, the correct answer is:
A. (-0.2, 1)
We have the following system of equations:
x + y = 0.8
4x + y = 0.2
To eliminate the y term, let's multiply the first equation by -1:
-1(x + y) = -1(0.8)
-x - y = -0.8
Now, we have:
-x - y = -0.8
4x + y = 0.2
Adding the two equations together, we can eliminate the y term:
(-x - y) + (4x + y) = -0.8 + 0.2
Simplifying, we get:
3x = -0.6
Dividing both sides by 3:
x = -0.2
Now, substitute the value of x back into one of the original equations, let's use the second equation:
4(-0.2) + y = 0.2
-0.8 + y = 0.2
y = 1
Therefore, the solution to this system of equations is (x, y) = (-0.2, 1).
Therefore, the correct answer is:
A. (-0.2, 1)
wrong
Apologies for the mistake. Let's solve the system correctly.
First
First
what? that's not an answer choice