Module 1 Pre-Lesson 30: Linear Systems in Two Variables

Warm Up: There are three methods for solving a system of equations in 2

variables: substitution, elimination, graphing. Do each one for the following

system:

Example 1:

2x + 3y = 7 2x + y = 3

Substitution: Elimination: Graphing

Procedures:

Substitution:

Solve one equation for a variable.

Substitute the equation into the other.

Solve for first variable.

Plug into other equation and solve for second variable.

Elimination:

If necessary, multiply one or both equations so that coefficient matches.

Add or subtract equations.

Solve for first variable.

Plug into other equation and solve for second variable.

Example 2:

5𝑥 −2𝑦 = 4 −2𝑥 + 𝑦 = 2

Example 3:

-16x + 7y = -18 8x – 8y = 0

Example 4:

5x – 14y = -2 -2x +7y = -2

Example 5:

-x – 5y = -26 -5x + y = 0

Exit Ticket:

Solve using substitution, elimination, and graphing:

3x – 6y = 30 5x – 2y =18