System of equations-5x+3y=-6 9x-4y=1

We can solve this system of equations by reduction method.

9(-5x+3y=-6)
5(9x-4y=1)

         7y=-49      ⇒y=-49/7=-7

4(-5x+3y=-6)
3(9x-4y=1)

   7x=-21          ⇒x=-21/7=-3

x=-3, y=-7

We can solve this system of equations by substitution method.

-5x+3y=-6      ⇒y=(-6+5x)/3
9x-4y=1

9x-4(-6+5x)/3=1
9x+(24-20x)/3=1
27x+24-20x=3
7x=3-24
7x=-21
x=-21/7=-3

y=(-6+5x)/3
y=(-6+5(-3))/3=(-6-15)/3=-21/3=-7

x=-3, y=-7