solve the system of equations Thank you

2x-y=3

x+2y=-6

multiply the second equation by -2

-2x-4y=12

add the first equation and the new second equation

2x-y=3

-2x-4y=12

-5y=15

y=-3

substitute into the first equation

2x-(-3)=3

2x+3=3

2x=0

x=0

solution:(0,-3)

using substitution...

2x-y=3

x+2y=-6

x=-2y-6

substitute into the first equation

2(-2y-6)-y=3

-4y-12-y=3

-5y-12=3

-5y=15

y=-3 again,

substitute into the first equation

2x-(-3)=3

2x+3=3

2x=0

x=0 again

these are just two ways to solve the problem; you can solve it in other ways:you can multiply the first equation by 2 and take it from there or solve for y in the first equation and then substitute into the second equation