Question
Solve the system of two equations using substitution.
y = 2 + 3x
4x - 3y = - 16
A. (2, 8)
B. (2, 10)
C. (-2, -4)
D. (-2, 4)
y = 2 + 3x
4x - 3y = - 16
A. (2, 8)
B. (2, 10)
C. (-2, -4)
D. (-2, 4)
Answers
Answer
Solve the system of equations.
2x + 6y = - 18
x = 5y - 1
A. (5.25, 1.25)
B. (-7.25, -1.25)
C. (4, 1)
D. (-6, - 1)
2x + 6y = - 18
x = 5y - 1
A. (5.25, 1.25)
B. (-7.25, -1.25)
C. (4, 1)
D. (-6, - 1)
Answer
Solve the system of equations.
3x + y = 2
7x - 4y = 30
A. (1/2, 1/2)
B. (2, - 2)
C. (2, - 4)
D. (-2, 8)
3x + y = 2
7x - 4y = 30
A. (1/2, 1/2)
B. (2, - 2)
C. (2, - 4)
D. (-2, 8)
Answer
Solve the system of equations.
- 4x + 6y = 38
x - 5y = -20
A. (-35, - 3)
B. (5, 3)
C. (-5, 3)
D. (35, - 3)
- 4x + 6y = 38
x - 5y = -20
A. (-35, - 3)
B. (5, 3)
C. (-5, 3)
D. (35, - 3)
Answer
How many solutions(s) does the system of equations have?
-5x + y = - 18
10x = 2y = 36
A. two
B. infinite
C. one
D. none
-5x + y = - 18
10x = 2y = 36
A. two
B. infinite
C. one
D. none
Answered by
GPT 3.5
We can solve the system of equations using substitution by substituting the expression for y in the second equation with the expression for y from the first equation.
y = 2 + 3x
Substituting this into the second equation:
4x - 3(2 + 3x) = -16
Expanding and simplifying:
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
Substituting this value of x back into the first equation:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8).
The correct answer is A. (2, 8)
y = 2 + 3x
Substituting this into the second equation:
4x - 3(2 + 3x) = -16
Expanding and simplifying:
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
Substituting this value of x back into the first equation:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8).
The correct answer is A. (2, 8)
Answered by
GPT 3.5
We can solve the system of equations by substituting the expression for x from the second equation into the first equation.
x = 5y - 1
Substituting this into the first equation:
2(5y - 1) + 6y = -18
Simplifying:
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Substituting this value of y back into the second equation:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is (-6, -1).
The correct answer is D. (-6, -1)
x = 5y - 1
Substituting this into the first equation:
2(5y - 1) + 6y = -18
Simplifying:
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Substituting this value of y back into the second equation:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is (-6, -1).
The correct answer is D. (-6, -1)
Answered by
GPT 3.5
We can solve the system of equations using either the method of substitution or elimination.
Method 1: Substitution
From the first equation, we can isolate y:
y = 2 - 3x
Substituting this expression for y into the second equation:
7x - 4(2 - 3x) = 30
Simplifying:
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Substituting this value of x back into the first equation:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).
The correct answer is C. (2, -4)
Method 2: Elimination
We can multiply both sides of the first equation by 4 and both sides of the second equation by 1 to eliminate the y variable:
12x + 4y = 8
7x - 4y = 30
Adding these two equations together eliminates the y terms:
19x = 38
x = 2
Substituting this value of x back into the first equation:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).
The correct answer is C. (2, -4)
Method 1: Substitution
From the first equation, we can isolate y:
y = 2 - 3x
Substituting this expression for y into the second equation:
7x - 4(2 - 3x) = 30
Simplifying:
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Substituting this value of x back into the first equation:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).
The correct answer is C. (2, -4)
Method 2: Elimination
We can multiply both sides of the first equation by 4 and both sides of the second equation by 1 to eliminate the y variable:
12x + 4y = 8
7x - 4y = 30
Adding these two equations together eliminates the y terms:
19x = 38
x = 2
Substituting this value of x back into the first equation:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).
The correct answer is C. (2, -4)
Answered by
GPT 3.5
We can solve the system of equations using either the method of substitution or elimination.
Method 1: Substitution
From the second equation, we can isolate x:
x = 5y - 20
Substituting this expression for x into the first equation:
-4(5y - 20) + 6y = 38
Simplifying:
-20y + 80 + 6y = 38
-14y = -42
y = 3
Substituting this value of y back into the second equation:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is (-5, 3).
The correct answer is C. (-5, 3)
Method 2: Elimination
We can multiply both sides of the second equation by 4 and both sides of the first equation by 1 to eliminate the x variable:
4x - 20y = -80
-4x + 6y = 38
Adding these two equations together eliminates the x terms:
-14y = -42
y = 3
Substituting this value of y back into the second equation:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is (-5, 3).
The correct answer is C. (-5, 3)
Method 1: Substitution
From the second equation, we can isolate x:
x = 5y - 20
Substituting this expression for x into the first equation:
-4(5y - 20) + 6y = 38
Simplifying:
-20y + 80 + 6y = 38
-14y = -42
y = 3
Substituting this value of y back into the second equation:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is (-5, 3).
The correct answer is C. (-5, 3)
Method 2: Elimination
We can multiply both sides of the second equation by 4 and both sides of the first equation by 1 to eliminate the x variable:
4x - 20y = -80
-4x + 6y = 38
Adding these two equations together eliminates the x terms:
-14y = -42
y = 3
Substituting this value of y back into the second equation:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is (-5, 3).
The correct answer is C. (-5, 3)
Answered by
GPT 3.5
To determine how many solutions the system of equations has, we can compare the number of equations and the number of variables.
In this case, the system consists of two equations and two variables.
The equations are:
-5x + y = -18
10x + 2y = 36
Since the number of equations is equal to the number of variables, we need to determine if the system is consistent (has a solution) or inconsistent (has no solution).
We can start by rearranging the second equation:
10x + 2y = 36
Divide both sides by 2:
5x + y = 18
Now we can compare the two equations:
-5x + y = -18
5x + y = 18
These two equations have the same coefficients and constant terms, but with opposite signs. This implies that they represent the same line.
Since the two equations represent the same line, the system is consistent and has infinite solutions.
The correct answer is B. infinite.
In this case, the system consists of two equations and two variables.
The equations are:
-5x + y = -18
10x + 2y = 36
Since the number of equations is equal to the number of variables, we need to determine if the system is consistent (has a solution) or inconsistent (has no solution).
We can start by rearranging the second equation:
10x + 2y = 36
Divide both sides by 2:
5x + y = 18
Now we can compare the two equations:
-5x + y = -18
5x + y = 18
These two equations have the same coefficients and constant terms, but with opposite signs. This implies that they represent the same line.
Since the two equations represent the same line, the system is consistent and has infinite solutions.
The correct answer is B. infinite.
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