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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:

  1. 2x + 7 = 20 is a linear equation in one variable, namely x.
  2. 3x - 4y = 5 is a linear equation in two variables, namely x and y.
  3. 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 ntequ.gif (849 bytes) 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

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