Solve the system of equations

9x - 4y = - 7

7x - 12y = 39

x?

y?

x = - 3

y = - 5

(-3, - 5)

Step-by-step explanation:

We can solve this system of equations by elimination. This is when you either add OR subtract the equations (depending on the situation) to eliminate one variable, allowing you to solve for the other. To do this, we need one variable with the same coefficient in BOTH equations.

9x - 4y = - 7 X3=> 27x - 12y = - 21 (New equation is still equivalent)

7x - 12y = 39

Both equations have negative "12y" in them. If you subtract - 12y from - 12y, you get 0, eliminating the variable. Subtract the two equations.

. 27x - 12y = - 21 Subtract each term in the equation.

- 7x - 12y = 39 Keep equal signs aligned

. 20x - 0 = - 60 'y' eliminated. - 12y - (-12y) = 0

. 20x = - 60 Isolate 'x'

. 20x/20 = - 60/20 Divide both sides by 20

. x = - 3 Solved for 'x'

Substitute 'x' for - 3 in any equation.

9x - 4y = - 7

9 (-3) - 4y = - 7 Substitute. Simplify multiplication.

-27 - 4y = - 7 Isolate 'y' now

-27 + 27 - 4y = - 7 + 27 Add 27 on both sides

-4y = 20 Left side cancelled out 27, right side simplified by adding.

-4y/-4 = 20/-4 Divide both sides by - 4

y = - 5 Solved for 'y'

Therefore the solution is when 'x' is - 3 (x = - 3) and when 'y' = - 5 (y = - 5).

You can also write the solution as an ordered pair, like coordinates, which are written (x, y). The solution would be (-3, - 5).