Systems of Linear Equations Using a Graph to Solve Math 10 F&P

In Biology, what does it mean by body system? When multiple organs interact for a common purpose ie. Digestive system

What do you notice? What do you wonder?

What do you notice? What do you wonder?

What do you notice? What do you wonder?

What is a System of Linear Equations? A system of linear equations is simply two or more linear equations using the same variables. If the system of linear equations is going to have a solution, then the solution will be an ordered pair (x , y) where x and y make both equations true at the same time.

What is a System of Linear Equations? If the lines are parallel, there will be no solutions. If the lines are the same, there will be an infinite number of solutions.

How to Use Graphs to Solve Linear Systems x y Graph the following system: x – 2y = –4 x + y = 5 Where do they intersect?

verify your ordered pair Verification You must ALWAYS verify your ordered pair x – 2y = –4 x + y = 5 x – 2y = –4 x + y = 5 (2, 3)

If the lines cross once, there will be one solution. If the lines are parallel, there will be no solutions. If the lines are the same, there will be an infinite number of solutions.

How to Use Graphs to Solve Linear Systems x y Solve the following system by graphing: 3x + 6y = 15 –2x + 3y = –3 Where do they intersect?

verify your ordered pair Verification You must ALWAYS verify your ordered pair 3x + 6y = 15 -2x + 3y = -3 3x + 6y = 15 –2x + 3y = –3 (3,1)

How to Use Graphs to Solve Linear Systems x y Solve the following system by graphing: 2x + 2y = 6 4x - 6y = 12 Where do they intersect?

verify your ordered pair Verification You must ALWAYS verify your ordered pair 2x + 2y = 6 4x - 6y = 12 2x + 2y = 6 4x - 6y = 12 (3,0)

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. Solve both equations for y, so that each equation looks like y = mx + b. Step 2: Graph both equations on the same coordinate plane. Use the slope and y - intercept for each equation in step 1. Be sure to use a ruler and graph paper! Step 3: Estimate where the graphs intersect. This is the solution! LABEL the solution! Step 4: Check to make sure your solution makes both equations true. Substitute the x and y values into both equations to verify the point is a solution to both equations.

To Do: KUTA worksheet We will mark together to make sure on right track 2. Booklet work through individually 3. Homework: 30 minutes of home practice tonight