Lesson 6

Solving Linear Equations Algebraically

 

Recall from your previous studies two algebraic methods used to solve a system of linear equations.

 

The following chart summarizes the main idea of each method.

 

Substitution	Elimination
Rearrange one of the equations for a single variable. Substitute the expression for the variable into the other equation.	Multiply the equations by constants such that the coefficients of the x-terms or the y-terms either match or have a sum of zero.

 

Try This 2

 

Consider the following linear-quadratic system.

 

y = −x2 + 3

x + 2y = 6

1. Solve the system by substitution.
   
   
2. Solve the system by elimination.
   
   
3. Verify your solutions. You may choose to do this by substituting the determined values into the original equations or by graphing.

Save your work in your course folder.

 

Share 2

 

There are four main ways of solving the system of equations from Try This 2—two variations each of substitution and elimination.

1. Compare your solutions from Try This 2 with a partner. Between the two of you, complete a table like the one shown by copying the appropriate solutions into the appropriate columns.
   
   
    

   Substitution: Isolate y	Substitution: Isolate x	Elimination: Eliminate y	Elimination: Eliminate x

   
   
2. For any solutions that are not covered by either your work or your partner’s work, consider together how you would solve the system by the method indicated. Then record your solutions in the appropriate columns.
   
   
3. Discuss which method(s) you prefer and give reasons why. Under what circumstances would you use some of the other methods that you did not prefer for the system in Try This 2?

Save your work in your course folder.