To solve the system of equations:
Equation 1: y = 5x + 7
Equation 2: 3y - 15x = 18
First, we can substitute Equation 1 into Equation 2 to get rid of the variable y.
3(5x + 7) - 15x = 18
15x + 21 - 15x = 18
21 = 18
This equation is not true, which means there is no solution to the system of equations.
y = 5x + 7
3y - 15x = 18
13 answers
y = 3x + 6
y = -13x - 4
y = -13x - 4
To solve the system of equations:
Equation 1: y = 3x + 6
Equation 2: y = -13x - 4
Since both equations are already solved for y, we can set them equal to each other:
3x + 6 = -13x - 4
Now, we can solve for x:
3x + 13x = -4 - 6
16x = -10
x = -10/16
x = -5/8
To find the value of y, we can substitute the value of x into either equation. Let's use Equation 1:
y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.
Equation 1: y = 3x + 6
Equation 2: y = -13x - 4
Since both equations are already solved for y, we can set them equal to each other:
3x + 6 = -13x - 4
Now, we can solve for x:
3x + 13x = -4 - 6
16x = -10
x = -10/16
x = -5/8
To find the value of y, we can substitute the value of x into either equation. Let's use Equation 1:
y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.
x - 2y = 6
3x - 6y = 18
3x - 6y = 18
To solve the system of equations:
Equation 1: x - 2y = 6
Equation 2: 3x - 6y = 18
We can solve this system of equations using the method of substitution or elimination. Here, we will use the method of elimination.
Step 1: Multiply Equation 1 by 3 to make the coefficients of x in both equations the same:
3(x - 2y) = 3(6)
3x - 6y = 18
Step 2: Now we can see that both equations have the same coefficient for x, which is 3. Subtract Equation 2 from Equation 1:
(3x - 6y) - (3x - 6y) = 18 - 18
0 = 0
Step 3: The equation 0 = 0 is true, which means that the two equations are equivalent and represent the same line. Thus, these equations have infinitely many solutions.
Equation 1: x - 2y = 6
Equation 2: 3x - 6y = 18
We can solve this system of equations using the method of substitution or elimination. Here, we will use the method of elimination.
Step 1: Multiply Equation 1 by 3 to make the coefficients of x in both equations the same:
3(x - 2y) = 3(6)
3x - 6y = 18
Step 2: Now we can see that both equations have the same coefficient for x, which is 3. Subtract Equation 2 from Equation 1:
(3x - 6y) - (3x - 6y) = 18 - 18
0 = 0
Step 3: The equation 0 = 0 is true, which means that the two equations are equivalent and represent the same line. Thus, these equations have infinitely many solutions.
y = 23x - 1
y = 23x - 2
y = 23x - 2
To solve the system of equations:
Equation 1: y = 23x - 1
Equation 2: y = 23x - 2
Since both equations are already in the form y = mx + b (slope-intercept form), we can see that they have the same slope, which is 23. This means that the lines are parallel and will never intersect.
Therefore, the system of equations has no solution.
Equation 1: y = 23x - 1
Equation 2: y = 23x - 2
Since both equations are already in the form y = mx + b (slope-intercept form), we can see that they have the same slope, which is 23. This means that the lines are parallel and will never intersect.
Therefore, the system of equations has no solution.
Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
What equation represent how much money Judy will have in total after saving for d days?
What equation represents how much money Elenore will have in total after saving for d days?
What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved? After the number of days it took both to have the same amount of money saved, how much money do they have each?
What equation represent how much money Judy will have in total after saving for d days?
What equation represents how much money Elenore will have in total after saving for d days?
What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved? After the number of days it took both to have the same amount of money saved, how much money do they have each?
The equation representing how much money Judy will have in total after saving for d days is:
Judy's saving = Judy's initial amount + (Judy's saving per day * number of days)
Judy's saving = $100 + ($5 * d)
Judy's saving = $5d + $100
The equation representing how much money Elenore will have in total after saving for d days is:
Elenore's saving = Elenore's initial amount + (Elenore's saving per day * number of days)
Elenore's saving = $75 + ($7 * d)
Elenore's saving = $7d + $75
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's saving = Elenore's saving
$5d + $100 = $7d + $75
To solve this equation for d, we can subtract $5d from both sides and subtract $75 from both sides:
$100 - $75 = $7d - $5d
$25 = $2d
Dividing both sides by $2:
$25/$2 = d
d = 12.5
Since we cannot have a fraction of a day, we can conclude that it will take 13 days for Judy and Elenore to have the same amount of money saved.
After 13 days, Judy will have:
Judy's saving = $5 * 13 + $100 = $165
After 13 days, Elenore will have:
Elenore's saving = $7 * 13 + $75 = $166
Judy's saving = Judy's initial amount + (Judy's saving per day * number of days)
Judy's saving = $100 + ($5 * d)
Judy's saving = $5d + $100
The equation representing how much money Elenore will have in total after saving for d days is:
Elenore's saving = Elenore's initial amount + (Elenore's saving per day * number of days)
Elenore's saving = $75 + ($7 * d)
Elenore's saving = $7d + $75
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's saving = Elenore's saving
$5d + $100 = $7d + $75
To solve this equation for d, we can subtract $5d from both sides and subtract $75 from both sides:
$100 - $75 = $7d - $5d
$25 = $2d
Dividing both sides by $2:
$25/$2 = d
d = 12.5
Since we cannot have a fraction of a day, we can conclude that it will take 13 days for Judy and Elenore to have the same amount of money saved.
After 13 days, Judy will have:
Judy's saving = $5 * 13 + $100 = $165
After 13 days, Elenore will have:
Elenore's saving = $7 * 13 + $75 = $166
The solution to a system of two linear equations is x = 3 weeks; y = 9 feet Match the description with the correct statement.
How could you get exactly two or three solutions to this linear system?
How would you locate the solution of the two linear graphs on the coordinate plane?
The solution to this system could possibly have this meaning.
How could you get exactly two or three solutions to this linear system?
How would you locate the solution of the two linear graphs on the coordinate plane?
The solution to this system could possibly have this meaning.
To get exactly two or three solutions to the linear system:
1. Introduce a third equation that intersects the other two equations at two or three different points. This will create a system of three equations with two or three solutions.
To locate the solution of the two linear graphs on the coordinate plane:
2. Graph the two linear equations on the same coordinate plane. The point(s) of intersection will represent the solution(s) to the system of equations.
The solution to this system could possibly have this meaning:
3. The solution represents the values of x and y that satisfy both equations simultaneously. In this case, x = 3 weeks and y = 9 feet represent a specific point of intersection for the two linear graphs. The meaning of this point depends on the context of the equations being solved.
1. Introduce a third equation that intersects the other two equations at two or three different points. This will create a system of three equations with two or three solutions.
To locate the solution of the two linear graphs on the coordinate plane:
2. Graph the two linear equations on the same coordinate plane. The point(s) of intersection will represent the solution(s) to the system of equations.
The solution to this system could possibly have this meaning:
3. The solution represents the values of x and y that satisfy both equations simultaneously. In this case, x = 3 weeks and y = 9 feet represent a specific point of intersection for the two linear graphs. The meaning of this point depends on the context of the equations being solved.
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
To check if the point (5, 6) is the solution to the Linear System of equations, you would substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
If after evaluating both equations with these substitutions, the resulting statements are true, then the point (5, 6) is indeed the solution to the system of equations.
If after evaluating both equations with these substitutions, the resulting statements are true, then the point (5, 6) is indeed the solution to the system of equations.