Question

Examine this system of equations. What integer should the first equation be multiplied by so that when the two equations are added together, the x term is eliminated?
1/18x + 4/5y = 10
-5/6x - 3/4y = 3

Answer 1

Hey there!

To find this, we should figure out what 1/18 can be multiplied by to get 5/6, because when we end up adding them together after multiplying, 5/6x - 5/6x eliminates x.

One thing that would make this easier is to make 1/18 and 5/6 have the same denominator.

6 goes into 18 3 times, so what we could do is multiply both the numerator and denominator of 5/6 by 3.

That gives us 15/18.

Now that we have the denominators the same, we can see that 1/18 goes into 15/18 15 times by comparing the numerators.

This means the first equation should be multiplied by 15.

Hope this helps!