How do you solve the following system?: -2x +5y =-6 , 5x +6y = -1

1 Answer
Jul 11, 2016

x = 31/37, y = -32/37

Explanation:

We can solve for y first by multiplying the first equation by 5 and the second equation by 2:

5(-2x + 5y) = (-6)5 and 2(5x + 6y) = (-1)2

Then we add the two equations, resulting in:

25y + 12y = -32, and therefore, 37y = -32

We divide both sides by 37, so y = -32/37

To solve for x, we multiply the first equation by -6 and the second equation by 5:

-6(-2x + 5y) = -6(-6) and 5(5x + 6y) = 5(-1)

Then we add the two equations, resulting in:

12x + 25x = 31, and therefore, 37x = 31

We divide both sides by 37, so x = 31/37

You can verify these answers by substituting 31/37 for x and -32/37 for y:

-2(31/37) + 5(-32/37) = -62/37 - 160/37 = -222/37 = -6