# Using the Substitution Method

Use Substitution to solve the system of equations

4x + y = 0
2y + x = -7

### Comments for Using the Substitution Method

Average Rating     Jan 17, 2011 Rating     Using the Substitution Method by: Karin In order to use the Substitution Method, you must first solve one of the equations for one variable. This means that you must rewrite one of the equations as x = ... or y=... It's easiest to solve equation 1 for y. 1. 4x+y = 0 2. 2y+x = -7 Step 1: Solve equation 1 for y by subtracting 4x from both sides. 4x-4x + y = 0-4x y = -4x Now that we know what y is equal to (-4x), we can substitute this into the 2nd equation. 2(-4x) +x = -7 Simplify: -8x +x = -7 Simplify further by combining x terms: -7x = -7 Divide by -7 to isolate the variable. -7x/-7 = -7/-7 x = 1 We now know that x is equal to 1, so we can substitute this for x and solve for y. I will use the new equation that I wrote: y = -4x y = -4(1) y = -4 Our solution is: (1, -4) I hope this helps! Karin