Solving
Linear Equations
x + y = 6 is an example of a linear equation in two variables.
Definition —
Linear Equation in Two Variables
A linear equation in two variables, x and y, is an equation that can
be written in the form
Ax By C
where A, B, and C are real numbers and A and B are not both 0.
A solution of a linear equation in two variables is an ordered pair that,
when substituted into the equation, results in a true statement.
A solution is said to satisfy the equation.
| A solution of the candy bar equation is
x = 4 and y = 2 since 4 + 2 = 6.
|
x + y = 6
4 + 2 = 6 |
|
This solution may be written as the
ordered pair (4, 2).
|
|
| The equation has other solutions,
including (3, 3) and (1, 5). |
3 + 3 = 6 1 + 5 = 6 |
Example 1
Determine if each ordered pair below is a solution of 2x + y = 4.
a. (-2, 8)
b. (5, 2)
| a. |
Solution Replace x with -2 and y with 8.
Simplify. |
2x + y
Is 2(-2) + 8
Is 4 |
= 4
= 4 ?
= 4? Yes |
| |
The ordered pair (-2, 8) is a solution of 2x
+ y = 4. |
|
| b. |
Replace x with 5 and y with 2.
Simplify. |
Is 2(5) + 2
Is 12 |
= 4?
= 4 ? No |
| |
Since 12 ≠ 4, the ordered pair (5, 2) is not a solution of 2x
+ y = 4. |
|
