-4x+y=6 [eq1]
-5x-y=21 [eq2]
To solve this system of equations using substitution, you must first solve for a variable in one equation, then substitute that expression into the other equation.
Solve for y in eq1:
y = 4x+6
Substitute that into eq2:
-5x - (4x+6) = 21
-9x - 6 = 21 [collect terms]
-9x = 27 [add 6 to both sides]
x = -3 [divide both sides by (-9)]
Now, substitute for x in either eq1 or eq2:
-4x+y=6 [eq1]
-4(-3) + y = 6
12 + y = 6
y = -6
Check (very important):
Is -4(-3)+(-6) = 6 ?
12 - 6 = 6 ?
6 = 6 ?yes
Is -5x-y=21 ?
-5(-3)-(-6) = 21 ?
15 + 6 = 21 ?
21 = 21 ?yes