Which of these strategies would eliminate a variable in the system of equations?

( 6x + 5y = 1

16x - 5y = 7

Choose all answers that apply:

B) Subtract the bottom equation from the top equation.

C) Add the equations.

Step-by-step explanation:

Let us analyze each of the options to see which one of them work.

A) Multiply the top equation by 7, then subtract the bottom equation from the top equation.

Multiplying the top equation by 7 gives:

7 * (16x + 5y) = (1 * 7)

112x + 35y = 7

Then, subtracting the bottom equation from this:

 112x + 35y = 7

-  (16x - 5y = 7)

=> 112x + 35y - 16x + 5y = 7 - 7

112x - 16x + 35y + 5y = 0

96x + 40y = 0

This method didn't eliminate any variable, so it didn't work for us.

B) Subtract the bottom equation from the top equation

This will yield:

  16x + 5y = 1

- (16x - 5y = 7)

=> 16x + 5y - 16x + 5y = 1 - 7

16x - 16x + 5y + 5y = -6

0x + 10y = -6

10y = -6

y = -6 / 10

Hence, one variable has been eliminated. It works.

C) Add the equations

This yields:

  16x + 5y = 1

+ 16x - 5y = 7

  32x + 0y = 8

  32x = 8

=>x = 8 / 32 = 1 / 4

This method works since one variable has been eliminated.