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 -6−6 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 -32/37−3237 for yy:
-2(31/37) + 5(-32/37) = -62/37 - 160/37 = -222/37 = -6−2(3137)+5(−3237)=−6237−16037=−22237=−6