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Question
2x - y = 5
3x + 2y = 4
Solve the system of equations.
Responses
A (0, 2)(0, 2)
B (2, -1)(2, -1)
C (3, 1)(3, 1)
D (97
, 177
)( 9 7 , 17 7 )
E (1, -3)(1, -3)
B (2, -1)(2, -1)
The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (12, -39)?
Responses
A 52
x + 23
y = 65 2 x + 2 3 y = 6
B 53
x + 23
y = 65 3 x + 2 3 y = 6
C 53
x + 23
y = -65 3 x + 2 3 y = -6
D 52
x + 23
y = -4
C 53 x + 23 y = -65 3 x + 23 y = -6
Solve the system of linear equations.
3x + 5y = −2
2x − y = 3
Responses
A (−1, 1)(−1, 1)
B (1, −1)(1, −1)
C (−1, −1)(−1, −1)
D (1, 1)
B (1, −1)(1, −1)
Find the equation of the line parallel to the line shown in the graph passing through the point (−2, 3).
Responses
A y = 32
x − 133
y = 3 2 x − 13 3
B y = 23
x + 133
y = 2 3 x + 13 3
C y = 32
x + 133
y = 3 2 x + 13 3
D y = 23
x − 133
Find the equation of the line perpendicular to the line shown in the graph passing through the point (−2, 3).
Responses
A y = 32
x − 3y = 3 2 x − 3
B y = −32
xy = − 3 2 x
C y = 32
xy = 3 2 x
D y = −32
x + 3y = − 3 2 x + 3
D y = −32x + 73
To solve the system of equations:
1. Start by choosing one of the equations and solving it for one variable in terms of the other variable. Let's choose the first equation and solve it for x:
2x - y = 5
2x = y + 5
x = (y + 5)/2
2. Now substitute this expression for x into the second equation:
3((y + 5)/2) + 2y = 4
(3/2)y + 15/2 + 2y = 4
(3/2)y + 2y = 4 - 15/2
(3/2 + 4/2)y = 8/2 - 15/2
(7/2)y = -7/2
y = -1
3. Substitute the value of y back into the equation we found in step 1 to solve for x:
x = (y + 5)/2
x = (-1 + 5)/2
x = 4/2
x = 2
4. So, the solution to the system of equations is x = 2 and y = -1. Therefore, the correct answer is B - (2, -1).