Using the Substitution Method

Use Substitution to solve the system of equations

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

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Jan 17, 2011
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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

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