pick a variable from system

Question

1. When solving the following system of equations by using the multiply-first method, which variable is easier to eliminate, and what should the multiplier be to help eliminate that variable?

12x+14y=25

3x+5y=5

Answer 1

Oooooh, man, this really confused me when I first learned it, so I understand.

 

What we need is for one variable to cancel out. How do we do that? We need the coefficients to be opposites so we can add them together and get 0.

 

15x + (-15x) = 0

 

Looking at our system, we could multiply the top by -5 and the bottom by 14 to get -70y + 70y, but it looks like it might be easier to multiply just the bottom by -4 so that we have 12x + (-12x).

 

I know it doesn't ask you to keep going, but I'll show you how it works.

 

12x + 14y = 25

-12x - 20y = -20

 

If we add those together, we get...

 

-6y = 5

y = -5/6

 

We would then plug -5/6 in to either equation and solve for x.

 

Soooo, the x is easier to eliminate, and we would multiply the bottom equation by -4.

 

Hope this helps!