Question

A system of two linear equations is shown below 2x+3y=8, 4x+4y=8 Henrietta claims that replacing the equation 2x+3y=6 with a different equation sometimes produces a system with the same solutions. Select three equations that can be used to support Henrietta's claim.

A. 3x+7y=14
B. 23−8y=−16
C. 4x−5y=−10
D. −2+15y=30

Answer 1

To support Henrietta's claim, we need to find equations that have the same solutions as the given system of equations. Options A and C can be used, but option B cannot. Therefore, the three equations that can be used are A. 3x + 7y = 14, C. 4x - 5y = -10, and the original equation 2x + 3y = 8.

Step-by-step explanation:

To support Henrietta's claim, we need to find equations that have the same solutions as the given system of equations. This means that when we solve the equations, the values of x and y will be the same. Let's test the three options:

A. 3x + 7y = 14

Plugging in the values from the given system of equations, we get:
2x + 3y = 8
3x + 7y = 14
This system of equations has the same solutions.

B. 23 - 8y = -16

Plugging in the values from the given system of equations, we get:
2x + 3y = 8
23 - 8y = -16
This system of equations has different solutions.

C. 4x - 5y = -10

Plugging in the values from the given system of equations, we get:
2x + 3y = 8
4x - 5y = -10
This system of equations has the same solutions.

Based on these results, options A and C can be used to support Henrietta's claim. So, the three equations that can be used are A. 3x + 7y = 14, C. 4x - 5y = -10, and the original equation 2x + 3y = 8.