Question

Ralph is trying to solve the system of equations. He begins by subtracting Ax from both sides of equation (1), and then he divides the equation by B. Before he can continue, his friend Alice comes along and says, "No, you should have subtracted By from both sides, and then divided by A. You will get the wrong answer." Is Alice right? Why or why not?

A) Yes; Ralph's way will make y disappear, resulting in no solution.
Eliminate
B) Yes; Ralph should isolate x in both equations. Now his answer will be wrong.
C) No; Ralph is substituting for y, Alice is substituting for x. Both ways will work.
D) No; Ralph is using substitution, while she is trying to use elimination. Both ways will work.

Answer 1

C) No; Ralph is substituting for y, Alice is substituting for x. Both ways will work.

Explanation:

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Answer 2

The correct answer is C.

Ralph's method will isolate the variable y, which he can then substitute into equation 2.

Alice's method will isolate the variable x, which she can then substitute into equation 2.

Regardless of which variable you substitute, you will end up with the same answer. Ralph's method will give him the value of x first, while Alice's method will give her the value of y first.