Use the table to answer the question
Which of the following equations, when combined with System B's equation, will make System A and System B have the same solution?
(1 point)
Responses
8x+4y=−16
8 x plus 4 y is equal to negative 16
x−12y=2
x minus 1 half y is equal to 2
−3x+y=8
negative 3 x plus y is equal to 8
x+3y=18
x plus 3 y is equal to 18
To find which equation combined with System B's equation will make System A and System B have the same solution, we need to look at the coefficients of x and y in each equation in System A and System B.
System A:
3x - 4y = -6
System B:
2x - 3y = -6
From System A and System B, if we multiply System B's equation by 3, we get:
6x - 9y = -18
Therefore, the equation that, when combined with System B's equation, will make System A and System B have the same solution is:
6x - 9y = -18
wrong
I apologize for the mistake. Let's evaluate the possible equations to find the one that, when combined with System B's equation, will make System A and System B have the same solution.
Given System A:
3x - 4y = -6
Given System B:
2x - 3y = -6
By comparing the coefficients, we can see that when we multiply System B's equation by 3, we get values that match System A's equation:
3(2x - 3y = -6)
= 6x - 9y = -18
Therefore, the equation that, when combined with System B's equation, will make System A and System B have the same solution is:
6x - 9y = -18