How do you solve the following system?: -2x +5y =-6 , 5x +6y = -12x+5y=6,5x+6y=1

1 Answer
Jul 11, 2016

x = 31/37, y = -32/37x=3137,y=3237

Explanation:

We can solve for yy first by multiplying the first equation by 55 and the second equation by 22:

5(-2x + 5y) = (-6)55(2x+5y)=(6)5 and 2(5x + 6y) = (-1)22(5x+6y)=(1)2

Then we add the two equations, resulting in:

25y + 12y = -3225y+12y=32, and therefore, 37y = -3237y=32

We divide both sides by 3737, so y = -32/37y=3237

To solve for xx, we multiply the first equation by -66 and the second equation by 55:

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

Then we add the two equations, resulting in:

12x + 25x = 3112x+25x=31, and therefore, 37x = 3137x=31

We divide both sides by 3737, so x = 31/37x=3137

You can verify these answers by substituting 31/373137 for xx and -32/373237 for yy:

-2(31/37) + 5(-32/37) = -62/37 - 160/37 = -222/37 = -62(3137)+5(3237)=623716037=22237=6