Solving Linear Equations

Definition: A linear equation looks like any other equation. It is made up of two expressions set equal to each other.

A linear equation is special because:
1) It has one or two variables.
2) No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

When you solve a linear equation, you need to isolate the variable you are solving for. To do this, you need to get the variable by itself on one side of the equals sign and the numbers on the other side. Remember, whatever you do to one side of a equation you must do to the other side.

To solve a system of linear equations, you must solve for one of the variables and then plug the value for that variable into the other equation.

Example: Solve for X and Y:
x + y = 6
−3x + y = 2

Solution: 

Step 1: Isolate Y (or x!) in one of the equations. In this case, the first equation is the easiest to do this to. So we have y = 6 – x

Step 2: Since we just found out that y = 6 – x, plug 6-x in for y in the second equation so that it now equals -3x + 6 – x = 2

Step 3: Simplify -3x + 6 – x =2. You get -4x=-4. Solve for x and you get x=-1

Step 4: Now plug in -1 for x in either of the equations to solve for y. So -1 + y = 6. Therefore, y=7.

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