Objective The student will be able to: solve systems of equations by graphing.

What is a system of equations? A system of equations is when you have two or more equations using the same variables. A system of two linear equations in two variables x and y has the form: y = mx + b A solution to a system of linear equations in two variables is an ordered pair that satisfies both equations in the system. When graphing, you will encounter three possibilities.

Solving a system of linear equations by graphing Rewrite each equation in slope- intercept form – y=mx + b. Determine the slope and y-intercept and use them to graph each equation. The solution to the linear system is the ordered pair where the lines intersect.

Intersecting Lines The point where the lines intersect is your solution. The solution of this graph is (1, 2) (1,2)

Y = 1/2x + 5 Y = -5/2x - 1 Examples

Y = -3/2x + 1 Y = 1/2x - 3 Examples

Parallel Lines These lines never intersect! Since the lines never cross, there is NO SOLUTION! Parallel lines have the same slope with different y-intercepts.

Coinciding Lines These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! Coinciding lines have the same slope and y-intercepts.

Y = 2/3x - 5 Y = 2/3x + 1 How many solutions?

Y = 3x - 12 Y = 1/8x - 12 How many solutions?

Y = 5/3x - 2 Y = 10/6x - 2 How many solutions?

Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Step 2: Do the graphs intersect? Step 3: Check your solution. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! This is the solution! LABEL the solution! Substitute the x and y values into both equations to verify the point is a solution to both equations.