Question

In order to slove the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them?

4x-2y=7
3x-3y=15


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Answer 1

B.

Explanation:

Multiply the top equation by -3 and the bottom equation by 2

-12x+6y=-21
6x-6y= 30
-6x = 9 Variable "y" is removed

Hope this helps

Answer 2

B. use multipliers -3 and 2

Explanation:

If you're solving the system by "addition," multiplying the equations by the chosen numbers needs to result in opposite coefficients for one of the variables.

Effect of answer choices

A. The system becomes ...

• 12x -6y = 21
• 12x -12y = 60

No variable has opposite coefficients.

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B. The system becomes ...

• -12x +6y = -21
• 6x -6y = 30

The y-variable has opposite coefficients. This is a good choice.

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C. The system becomes ...

• 12x -6y = 21
• 6x -6y = 30

No variable has opposite coefficients.

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D. The system becomes ...

• 4/3x -2/3y = 7/3
• 3x -3y = 15

No variable has opposite coefficients.

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Additional comment

The simplest "no brainer" solution is to use the coefficients of one of the variables, negating one of them. Multiply each equation by the opposite equation's coefficient. Here, the y-coefficients are -2 and -3, and the multipliers of answer choice B are -3 and 2, consistent with this advice. (The sign of 2 was changed.)