Solutions to Linear Equations in Two Variables
In this section
we will learn to use that same technique to determine if given values as points (x, y) make a
true
statements of linear equations in two variables. These points are called solutions or
truth values.
We will also build tables as sequences of truth values.
EXAMPLES:
1. Given 2x − 3y = 6 use the replacement values for the points (x, y) to see if the points lie on the
line defined by the equation. [That is, see if the points make a true statement of the equation.]
Do the points (3, 0), (3, 3) , (0, 2), (6, 2) satisfy the equation?
Use the points as replacements:
2(3) − 3(0) = 6 ?? 
6 − 0 = 6

This point is on the line. 
2(3) − 3(3) = 6 ?? 
6 − (9) ≠ 6

This point is not on the line. 
2(0) − 3(2) = 6 ?? 
0 − (6) = 6

This point is on the line. 
2(6) − 3(2) = 6 ?? 
12 − 6 = 6

This point is on the line. 
2. Given 5x + 2y = 10 use the replacement values for the points (x, y) to see if the points lie on
the line defined by the equation. [That is, see if the points make a true statement of the
equation.]
Do the points (2, 0), (2, 10), (4, 2) (0, 5) satisfy the equation?
Use the points as replacements:
5(2) + 2(0) = 10 ?? 
10 + 0 = 10

This point is on the line. 
5(2) + 2(10) = 10 ?? 
10 + 20 = 10

This point is on the line. 
5(4) + 2(2) = 10 ?? 
20 + ( 4) ≠ 10

This point is not on the line. 
5(0) + 2(5) = 10 ?? 
0 + 10 = 10

This point is on the line. 
NOTE: This method can be used to check your points and solutions to applications.
