Warm Up Write the equation of the line that is parallel to y = 3x +7 and goes through the point (-2, 5) Determine if the following equations represent parallel, perpendicular, intersecting (but not perpendicular), or coinciding lines: 2. 3. 4.

Warm-Up Answers: y = 3x +b 5 = 3(-2) + b 5 = -6 + b 11 = b y = 3x +11 2. Perpendicular 3. Intersecting Not Perpendicular 4. Coinciding

Solving systems of equations using substitution Lesson 7.3 Solving systems of equations using substitution

SUBSTITUTION! (And it’s going to be awesome!) Recap: We have discussed what a solution to a system of equations looks like, and how to find it by graphing. Today we are going to learn a new method for solving systems of equations…. SUBSTITUTION! (And it’s going to be awesome!)

Key words System of Equations Two or more equations System Solution A point (x, y) that satisfies both equations Substitution Replacing one variable with an equivalent expression

5 Simple Steps To finding the Solution: Solve one equation for either x or y Substitute the expression into the other equation Solve for the variable Substitute the value back in and solve Write your solution as an ordered pair. Check your answer, is it a solution? Remember that a point consists of an “x” value and a “y” value. You have to find BOTH to find the solution!

Example #1 Step Already done! Solve one equation for x or y y = x + 1

Step Substitute that expression into the other equation Equation 1: y = x + 1 Equation 2: y = -2x - 2 Resulting Equation: x + 1 = -2x - 2

Step Solve for the remaining variable +2x +2x 3x + 1 = -2 3x = -3 - 1 - 1 3x = -3 3 3 x = -1

Step Substitute the value back in and solve for the other variable y = -1+ 1 y = 0 Step (-1,0) Is (-1, 0) a solution? Check to find out. 0 = -1 + 1 0= -2(-1) – 2 Solution (-1, 0)

You Try This One Ex. 2 y = x + 4 y = 3x + 10 Solution (-3, 1)

Substitution and the Distributive Property Whenever you substitute an expression into another equation, be sure to keep it wrapped up in parentheses as a reminder to distribute! Ex. 3 2x – y = 1 Now substitute back into the equation that is solved for the other variable: y = 2 + 1 y = 3 2x-(x+1) =1 2x –x -1 =1 x -1 = 1 x = 2 y = x+1 Solution: (2, 3)

Your Turn: Solve the following systems of equations. 1. y = x +1 7x – 2y = 15 (2, 3) (5, 10)

What does it look like if there are infinite solutions, or no solutions? Let’s take a look… 1. -14x + 2y = 6 y = 7 + 7x 2. y = x - 5 -2x + 2y = -10 No Solution Infinite Solutions

Summary: Explain why it is important to keep the expression you substitute into the other equation wrapped in parentheses.

Substitution Revolution! Class Activity: Substitution Revolution! Your teacher will pass out a note card to each of you. Once you have your note card, write down an equation in 2 variables (Ex. y =-3x +9). The equation can be anything you want, but please keep the numbers in front of the variables between -6 and 6. When everyone has their equation break into 2 lines and begin substituting with the person across from you (this means everyone should have a sheet of lined paper out to show your work and turn into your teacher at the end of class). Once everyone is done solving the revolution begins…and you will substitute your equation with the next person across from you!

Homework: Worksheet 7.3