Solving systems of equations by elimination

-4x+9y=9

X-3y=-6

Manipulate the equations until one of the variables match up

I'm going to cancel the y-values.

-4x+9y=9

x-3y=-6

the way to do that is to multiply all the numbers, on both sides of the equation, by 3.

3 (x-3y) = 3 (-6)

3x-9y=-18 Now that the y value matches up with the other one, add the 2 equations

-4x+9y=9

+ 3x-9y=-18

The resulting equation is - x=-9, so x=9.

Plug this new x-value into one of the original equations to find the y-value.

x-3y=-6

(9) - 3y=-6

-3y=-15, so y=5

Check your work by plugging the 2 variables into both equations and the results should both be true.

-4 (9) + 9 (5) = 9 - 36+45=9 9=9

(9) - 3 (5) = - 6 9-15=-6 - 6=-6

So y=5 and x=9