is (9,6) a solution of the system of linear equations

We can always tell if something is a solution.....if we "plug" it in and it "works,"  then.....it must be the solution !!

So we have

-3x+y=-21

 x+y=3        

Notice that we can rewrite the second equation as y = 3 - x    and substituting this into the first equation for y, we have

-3x + (3 - x)  = -21  simplify

-4x + 3  = -21     subtract 3 from both sides

-4x = -24       divide both sides by -4

x = 6

And putting this into y = 3 - x  ... we have ....   y = 3 - 6  = -3

So the solution is  (6, -3)

You should check that this is correct by substituting these values into both equatons.....