Big Ideas Math: Modeling Real Life, Grade 8
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2. Solving Systems of Linear Equations by Substitution
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Exercise 1 Page 206

When solving a system of equations using the Substitution Method, there are three steps.

  1. Isolate a variable in one of the equations.
  2. Substitute the expression for that variable into the other equation and solve.
  3. Substitute this solution into one of the equations and solve for the value of the other variable.
For this exercise, is already isolated in both equations, so we can skip straight to solving! Since the expression equal to in (II) is simpler, let's use that for our initial substitution.
Subtract terms
Calculate quotient
Great! Now, to find the value of we need to substitute into either one of the equations in the given system. Let's use the second equation.
The solution, or point of intersection, to this system of equations is the point

Checking Our Answer

To check our answer, we will substitute our solution into both equations. If doing so results in true statements, then our solution is correct.

,

Identity Property of Multiplication

Because both equations are true statements, we know that our solution is correct.