Notice that the x coefficients are opposite in the two equations (in the first equation it's -1, in the seconds it's 1). So, if we sum the two equations, we will cancel out the x variable:
[tex]\underbrace{(-x+3y)+(x+y)}_{\text{sum of LHS}}=\underbrace{-15+(-9)}_{\text{sum of RHS}}[/tex]
This equation works out to be
[tex]4y=-24 \iff y=\dfrac{-24}{4}=-6[/tex]
Now that we know the value for y, we can plug it into one of the two equations. The second one looks simpler, so we have
[tex]x+y=-9 \iff x-6=-9 \iff x=-3[/tex]
