System Of Equations

Question

What is a possible first step in eliminating a variable in the following system of equations?

5x + 2y = 2
8x - y = -22         Choose one answer.

A. Multiply the first equation by 2.
 

B. Multiply the second equation by 2.
 

C. Multiply the first equation by -2.
 

D. Multiply the second equation by -2.

Answer 1

Since we are looking to eliminate a variable we want either the x or y variable to cancel out.

 

Looking at the answers we can see that we are only given the option to multiply by 2 or -2 so we can't be dealing with x because 5x x 2 or 5x x -2 will not cancel a positive 8x and 8x x 2 or 8x x -2 will not cancel a positive 5x.

 

Looking at the y variables we see that multiplying the first equation by 2 will not cancel the y in the second equation so we know we must multiply the second equation by either 2 or -2. 

 

Since the first equation has a +2y and the second equation has a -y we know that the only option to get rid of the y variable is to multiply the second equation by 2 to get -2y.

 

Therefore the answer is B.