Concept Byte: Solving Systems Using Algebra Tiles

Use With Lesson 6-2

ACTIVITY

Just as algebra tiles can help you solve linear equations in one variable, they can also help you solve systems of linear equations in two variables.

Model and solve the system.

Equation	Algebra Tiles	Steps
− x + 2 y = 4 negative x plus 2 y equals 4 − x + 2 ( x + 1 ) = 4 negative x plus 2 open x plus 1 close equals 4 − x + 2 x + 2 = 4 negative x plus 2 x plus 2 equals 4		Substitute x + 1 for y in the first equation.
( − x + x ) + x + 2 = 4 open negative x plus x close plus x plus 2 equals 4 x + 2 = 4		Remove the zero pair x and − x . negative x .
x + 2 − 2 = 4 − 2 x plus 2 minus 2 equals 4 minus 2		Subtract 2 from each side. Remove zero pairs.
x = 2		Solve for x.
y = x + 1		Model the second equation.
y = 2 + 1 y = 3		Substitute 2 for x and simplify.

The solution of the system is (2, 3).

Exercises

Model and solve each system.

1. y = x + 1

   2x + y = 10

2. x + 4y = 1

   x + 4 = y

3. y = 2 x − 1 y equals 2 x minus 1

   y = x + 2

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