Question

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?

5x + 13y = 232

12x + 7y = 218

A.The first equation can be multiplied by –13 and the second equation by 7 to eliminate y.
B.The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
C.The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
D.The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

Answer 1

3rd one

Explanation:

Answer 2

C

Explanation:

So the system is:

5x+13y=232

12x+7y=218

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Let's look at the options to see which will work:

A) Multiply first equation by -13: -65x-169y=-3016

& second equation by 7 : 84x+49y=1526

There are no opposites in the either one of the variable columns so not this option.

B) Multiply first equation by 7: 35x+91y=1624

& second equation by 13 : 156x+91y=2834

There are no opposites in the either one of the variable columns so this is not option unless we were asked to subtract the equations.

C) Multiply first equation by -12: -60x-156y=-2784

& second equation by 5 : 60x+35y=1090

There is a column that contains opposites here so when you add the equations the x-variable will get eliminated.