Question

Solve each system using elimination x-3y=27 3x-3y=39

Answer 1

Divide the problem into 3 steps. 1.Eliminate one variable. 2. Solve for the remaining variable. 3. Use that information to solve for the second variable.
1.
Multiply the top equation by -3
-3x+9y=-81
3x-3y=39
If you add these two equations together, you are left with
6y=-42
2.
Solve for y by dividing both sides by 6
y=-7
3.
Plug -7 in for y in the either equation. I'll use the top one. It's just simpler.
x-3(-7)=27
x=6

Check your work plugging both variables into both equations to see if they are still true.

Answer 2

$x-3y=27 \ \ \ |\times (-1) \\ 3x-3y=39 \\ \\ -x+3y=-27 \\ \underline{3x-3y=39 \ \ \ \ \ } \\ 3x-x=39-27 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \\ \\ x-3y=27 \\ 6-3y=27 \\ -3y=27-6 \\ -3y=21 \\ y=\frac{21}{-3} \\ y=-7 \\ \\ \boxed{(x,y)=(6,-7)}$