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System of Equations: Substitution


A system of equations is a set of equations that are linked together. The simplest system of equations is two equations with two unknowns.

One way to solve a system of equations is by substitution:

  1. With one equation, solve for y in terms of x
  2. For the second equation, substitute y with the equation you solved for in step 1
    and solve for x


Example:

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)
-x + y = - 1
3x - 4y = 9		   First equation solved for y:
Answer (x,y):

Step 1: Solve for y
-x + y = - 1
-x + y + x = - 1 + x
y = x - 1

Step 2: Substitute and solve for x
3x - 4y = 9
3x - 4(x - 1) = 9
3x - 4x + 4 = 9
-x + 4 = 9
-x + 4 - 4 = 9 - 4
-x = 5
x = -5

Now solve for y
y = x - 1
  = -5 - 1
  = -6
The answer is   First equation solved for y:   Answer (x,y):

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