Question

If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?

x − y = 6
4x − 3y = 12

Answer 1

You have to make a 3y appear in your first equation, or, make the 3 disappear in the second equation.

Answer 2

\[\frac{4x − 3y = 12}{3}\rightarrow\frac{4}{3}x-y=4\]

Answer 3

Or, (x − y = 6)3 \(\rightarrow\) 3x-3y=18

Answer 4

Add the two equations together

Multiply the first equation by −4

Multiply the first equation by 3

Multiply the first equation by −3

Answer 5

Oh, adding up.

Then
(x − y = 6)-3=-3x+3y=-18