Systems of Linear Equations Method 1: Using a Graph to Solve Method 2 : Solve by Substitution Method 3 : Solve by Linear Combination / Elimination

What is a System of Linear Equations? A system of linear equations is simply two or more linear equations using the same variables. We will only be dealing with systems of two equations using two variables, x and y.y. If the system of linear equations is going to have a solution, then the solution will be an ordered pair (x (x, y) where x and y make both equations true at the same time. We will be working with the graphs of linear systems and how to find their solutions graphically.

Graphing to Solve a Linear System While there are many different ways to graph these equations, we will be using the slope - intercept form. To put the equations in slope intercept form, we must solve both equations for y. Now, we must graph these two equations. 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 Using the slope intercept form of these equations, we can graph them carefully on graph paper. x y Start at the y - intercept, then use the slope. Label the solution! (3, 1) We can write the answer as x=3 and y = 1 or as (3,1)

x y LABEL the solution! Graphing to Solve a Linear System 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. LABEL the solution! Let's do ONE more…Solve the following system of equations by graphing. 2x + 2y = 3 x – 4y = -1 x = 1 and y = 0.5 or (1, 0.5)

Graphing to Solve a Linear System Let's summarize! There are 3 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. 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 and write it as your answer!

If the lines cross once, there will be one solution. What if the lines are parallel? If the lines are parallel, there will be no solutions. What if the lines turn out to be the same line? If the lines are the same, there will be an infinite number of solutions.

HW pg. 309 #2 to 12 even