Warm-Up 1. Determine the mistake. Then correctly solve. 4x +6 = -3(x+ 4) step 1 4x +6 = -3x – 12 step 2 x +6 = -12 step 3 x = -18 step 4 2. Determine the number of solutions for the system of equations 2x + y = 4 and -10 – 2y = 4x

Agenda Warm-Up Review Homework Guided Notes on Solving Systems of Equations by Graphing Ticket out the Door

Quick Check! What is a systems of equations? What is an example of a system of equations?

Solving Systems of Equations Three ways to solve systems of equation By Substitution By Elimination By Graphing When we talk about the solution to a systems of equations we mean the values of the variables that make both equations true at the same time. When solving a systems of equations graphically, our solution is THE POINT OF INTERSECTION (where the two lines cross eachother).

Types of Solutions Independent system: a system that has A POINT OF INTERSECTION or in other words only ONE SOLUTION. Dependent system: a system that HAS MANY SOLUTIONS (The same line twice.)  Inconsistent system: a system that HAS NO SOLUTION.

Steps to Solving Systems of Equations Graphically Step 1: Put your equations in SLOPE-INTERCEPT FORM (y=mx+b) . Step 2: Graph the given equations by using what you know about SLOPE – INTERCEPT FORM. Step 3: Identify the point of intersection, or in other words your SOLUTION. Step 4: Prove that your solution makes both equations TRUE.

Example 1: Solve by graphing

Example 2: Solve by graphing

Guided Practice!

Independent Practice In pairs!

Ticket Out the Door 2x + y = 6 y = 2x - 2 Determine the number of solutions for the system of equations 5x – 2y = 8 and y = 5 2 x - 4 2. Solve the system of equations by graphing! Then determine if the system is independent, dependent or inconsistent! 2x + y = 6 y = 2x - 2