Free Algebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 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 = 61 + 5 = 6

Example 1

Determine if each ordered pair below is a solution of 2x + y = 4.

a. (-2, 8)

b. (5, 2)

 a. SolutionReplace 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.