Get y alone in 1st equation
-4x+y=6
-4x + 4x + y = 6 +4x
y= 4x+6
sub into 2nd equation
-5x-y=21
-5x-(4x+6)=21
-5x-4x-6=21
-9x-6=21
-9x-6+6=21+6
-9x=27
-9x/-9 = 27/-9
x=-3
sub into 1st equation
y=4x+6
y=4(-3)+6
y=-12+6
y=-6
Check your work
-4(-3)+(-6) =6
12 -6 =6
6=6
-5(-3)-(-6)=21
15-6=21
21=21