Solving
Linear Equations
x + y = 6 is an example of a linear equation in two variables.
Definition â€”
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. 
