Equations and Inequalities: System of Equations

A system of equations contains two equations and two variables.

For example, consider the system of equations: and

-  The easiest way to solve a system of equations is using the elimination method. The elimination method uses the addition property of equality. You can add the same value to each side of an equation.
-  For the first equation above, you can add to the left side and 5 to the right side of the first equation: . Now, if you simplify, you get: . Now, substitute 3 for the in the first equation: . By solving this equation,

Example:
What is the value of in this system of equations?

Solution: Solving a System of Equations by Elimination:

Multiply the first equation by then add it to the second equation.
⇒
Plug in the value of into one of the equations and solve for .

Thus,