A system of equations is defined as two or more equations that use the same variables. The solution to these equations, if one exists, is the point(s) of intersection between the lines.

To find the solution to a system of two equations by graphing:

Put the equations in slope-intercept form, if necessary.

Graph both equations on the same coordinate plane.

Plot the y-intercept

From the y-intercept, use the slope to find a second point on the line. Remember, rise over run!

Connect the points to graph the line.

Identify the point of intersection. The point of intersection is the solution to the system.

General Steps for Solving Systems of Equations by Elimination

1. Identify/Create opposite coefficients.

2. Add the equations vertically.

3. Simplify and solve for the first variable.

4. Substitute and solve. Substitute the value of the first variable into one of the original equations and solve for the second variable.

When both variables are eliminated and you are left with a …

True Equation

False Equation

Final answer: Infinitely Many Solutions

Final answer: No Solution

The two equations graph the same line.

The two equations graph parallel lines.

Lesson Summary

Steps for Using Substitution to Solve a System of Equations

Step 1. Isolate one variable of one equation.

Choose an equation and solve for one of the variables.

Step 2. Substitute and solve for one variable.

Substitute the expression for the…