How to Solve a Linear Equation

Linear equations

A linear equation has two expressions, separated by an equal sign, that equal each other. The solution to a linear equation is always a straight line, hence the name "linear" equation. Linear equations are easy to solve.

Things You'll Need

• Calculator
• Pen
• Paper

Instructions

1. Isolate the variable to one side of the equal sign. You do this by taking the constant (number) to the other side of the equal sign and changing its sign. Let us work with the equation 4x+3 = 19.
   4x+3-3 = 19-3
   4x = 16

2. Solve for x:

   4x=19-3
   4x=16
   x=16/4=4
   Check by plugging in the answer in the original equation:

   4x+3 = 19
   4*4+3 = 19
   19=19

3. Apply the same method if you have more than one variable in the equation. For example:

   2x-2y = 16
   2x-2y+2y = 16+2y [Isolating the variable]
   2x=16+2y [Isolating the variable]

   x=16+2y/2 [Solving for x]
   x=8+y [Solving for x]

   2*(8+y)-2y=16 [Checking the solution]
   16+2y-2y=16 [Checking the solution]
   16=16 [Checking the solution]

4. Solve using the same steps even if there is a fraction involved:

   2/6y = 20
   2/6*6/2y = 20*6/2 [Isolating the variable]
   y = 60 [Solving for y]
   2/6*60 = 20 [Checking the solution]
   20=20 [Checking the solution]

Tips & Warnings

• In a linear equation you cannot divide or multiply one variable by another.

• The variable cannot be squared or be the square root of some number.

References

• PurpleMath: Solving Linear Equations
• SOSMath: Linear Equations