Presentation on theme: "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."— Presentation transcript:
1Warm UpWrite 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:
2Warm-Up Answers: y = 3x +b 5 = 3(-2) + b 5 = -6 + b 11 = b y = 3x +11 2. Perpendicular3. Intersecting Not Perpendicular4. Coinciding
3Solving systems of equations using substitution Lesson 7.3Solving systems of equations using substitution
4SUBSTITUTION! (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!)
5Key words System of Equations Two or more equations System Solution A point (x, y) that satisfies both equationsSubstitutionReplacing one variable with an equivalent expression
65 Simple Steps To finding the Solution: Solve one equation for either x or ySubstitute the expression into the other equationSolve for the variableSubstitute the value back in and solveWrite 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!
7Example #1 Step Already done! Solve one equation for x or y y = x + 1
8Step Substitute that expression into the other equation Equation 1: y = x + 1Equation 2: y = -2x - 2Resulting Equation: x + 1 = -2x - 2
10StepSubstitute the value back in and solve for the other variabley = -1+ 1y = 0Step (-1,0)Is (-1, 0) a solution? Check to find out.0 =0= -2(-1) – 2Solution (-1, 0)
11You Try This OneEx. 2y = x + 4y = 3x + 10Solution (-3, 1)
12Substitution 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. 32x – y = 1Now substitute back into the equation that is solved for the other variable:y = 2 + 1y = 32x-(x+1) =12x –x -1 =1x -1 = 1x = 2y = x+1Solution: (2, 3)
13Your Turn: Solve the following systems of equations. 1. y = x +1 7x – 2y = 15(2, 3)(5, 10)
14What does it look like if there are infinite solutions, or no solutions? Let’s take a look… x + 2y = 6y = 7 + 7x2. y = x - 5-2x + 2y = -10No SolutionInfinite Solutions
15Summary:Explain why it is important to keep the expression you substitute into the other equation wrapped in parentheses.
16Substitution 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!