What is the solution to

-4x+5y=-12

x-6y=22

The solution to the system is S = (-2, - 4).

Step-by-step explanation:

Given the system

-4x+5y=-12

x-6y=22

The first step is to solve x from the first equation for example, and substitute the expression in the second equation.

1) - 4x + 5 y = - 12 ⇒ - 4x = - 12 - 5y ⇒ x = (-12 - 5y) / -4 ⇒ x = 3 + (5/4) y

2) x - 6y = 22 ⇒ (3 + (5/4) y) - 6y = 22 ⇒ 3 + (5/4) y - 6y = 22

⇒ 3 - (19/4) y = 22 ⇒ (-19/4) y = 22 - 3 ⇒ y = 19 / (-19/4) ⇒ y = -4.

Finally, with the value obtained for "y", you have to return to the original equations and replace it to obtain the "x" value.

-4x + 5y = - 12 ⇒ - 4x + 5 (-4) = - 12 ⇒ - 4x - 20 = - 12 ⇒ - 4x = - 12 + 20

⇒ - 4x = 8 ⇒ x = 8/-4 ⇒ x = - 2.

Summarizing, the solution to this system is S = (-2, - 4).