Solving
Linear Equations
We can use the following procedure to find a solution of a linear equation
in two variables.
Procedure —
To Find a Solution of a Linear Equation in Two Variables
Step 1 Choose a value for one of the variables and substitute it in
the equation.
Step 2 Solve the equation for the remaining variable.
Step 3 Write the numbers from Step 1 and Step 2 as an ordered
pair.
Example 1
Find a solution of 2x + y = 7.
Solution
Step 1 Choose a value for one of the variables and substitute it in the
equation.
| We may select any real number for
x or y.
Let’s select 3 for x and substitute
it into the equation. |
2x + y = 7
2(3) + y = 7 |
Step 2 Solve the equation for the remaining variable.
| Simplify . Subtract 6 from both sides. |
6 + y = 7
y = 1 |
Step 3 Write the numbers from Step 1 and Step 2 as an ordered pair.
A solution of the equation 2x + y = 7 is (3, 1).
Example 2
Complete the table for the equation -3x + y = 4.
Solution
For each ordered pair, substitute the given value in the equation.
Then solve for the remaining variable.
| Let x = 2.
Substitute 2 for x.
Simplify.
Add 6 to both sides. Let y = -8.
Substitute -8 for y.
Add 8 to both sides.
Divide both sides by -3. |
-3x + y
-3(2) + y
-6 + y
y -3x + y -3x +
(-8) -3x x |
= 4 = 4
= 4
= 10 = 4 = 4 = 12 = -4 |
The completed data table looks like this:
|
