Quick Review 5-1

Unit 5 - Objective 1 - Linear Equations

A linear equation is the equation of a straight line. An equation is linear if each term contains only one variable to the first power or the term is a constant.

Examples:

2x + 7 = 20 is a linear equation in one variable, namely x.
3x - 4y = 5 is a linear equation in two variables, namely x and y.
4x + 3y - 2z = 5 is a linear equation in three variables, namely x, y, and z.

A solution is any set of numbers, one for each variable, which satisfies the equation.

Examples:

Given the linear equation 3x - 2y = 9

1.	Is	x = - 3
		y = 0
	a solution?

	3 (-3) - 2 (0) = 9 -9 - 0 = 9 - 9 9 No

2.	Is	x = 3
		y = 0
	a solution?

	3 (3) - 2 (0) = 9 9 - 0 = 9 9 = 9 Yes

There are many solutions that will satisfy this equation. If you are given a value for x you can determine the y value by solving the equation.

Examples:

1.	3x - 2y = 9 plug in 1 for x	x = 1
	3 (1) - 2y = 9 3 - 2y = 9 -2y = 6 y = - 3	so (1, -3) is a solution

2.	3x - 2y = 9 plug in 0 for y	y = 0
	3x - 2 (0) = 9 3x - 0 = 9 3x = 9 x = 3	So (3, 0) is a solution