Systems of Linear Equations Using a Graph to Solve

A System of Linear Equations has 2 or more equations. The equations have the same variables.

Three Types of Systems INDEPENDENT (Different Slopes) If the lines cross once, there will be one solution. INCONSISTENT(Same Slopes, different intercepts) If the lines are parallel, there will be no solutions. DEPENDENT(Same Slopes, same intercepts) If the lines are the same, there will be an infinite number of solutions.

How to Use Graphs to Solve Linear Systems x y x – y = –1 x + 2y = 5 The point where they intersect makes both equations true at the same time.

x – y = –1 x + 2y = 5 How to Use Graphs to Solve Linear Systems x y Consider the following system: (1, 2) We must ALWAYS verify that your coordinates actually satisfy both equations. To do this, we substitute the coordinate (1, 2) into both equations. x – y = –1 (1) – (2) = –1  Since (1, 2) makes both equations true, then (1, 2) is the solution to the system of linear equations. x + 2y = 5 (1) + 2(2) = = 5 

Graphing to Solve a Linear System Solve the following system by graphing: 3x + 6y = 15 –2x + 3y = –3

Graphing to Solve a Linear System Solve the following system by graphing: 3x + 6y = 15 –2x + 3y = –3 x y Label the solution! (3, 1)

Graphing to Solve a Linear System Let's summarize! There are 4 steps to solving a linear system using a graph. Step 1: Put both equations in slope - intercept form. Step 2: Graph both equations on the same coordinate plane. Step 3: Estimate where the graphs intersect. Step 4: Check to make sure your solution makes both equations true. Solve both equations for y, so that each equation looks like y = mx + b. Use the slope and y - intercept for each equation in step 1. 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.

P 120 #1-9, odd 13-23, odd