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Friday 13th of September
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Linear Equations

We can use the following procedure to find a solution of a linear equation in two variables.

Procedure â€” 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. Letâ€™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.

 x y 2 -8

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:
 x y 2 10 -4 -8