Verifying Solutions

Warm - Up To find your new seat, take a card and solve the problem. Then, follow the seating chart to see where your seat is located.

Table of Contents 4: Warm-Up, Guided Practice 5: How Do I Verify Solutions of Equations?

Warm - Up Determine if the following solutions are correct. Justify your answers 12 – 7c = 54 c = 6 2(3w + 4) = 5 w = -2

Warm - Up Determine if the following solutions are correct. Justify your answers 1. 12 – 7c = 54 2. 2(3w + 4) = 5 c = 6 w = -2 No, 6 is not a solution to the equation No, -2 is not a solution to the equation

Learning Intention/Success Criteria LI: We are learning to verify solutions to linear equations SC: I know how to -use the order of operations -show solutions to equations are in the form (x, y) -explain that solution to an equation is true if and only if it lies on the line of the equation -solve for an input value of a function corresponding to an specified output value, algebraically.

EQ: How Do I Verify Solutions to Equations? 9/17/2018

Parenthesis PEMDAS Exponents Multiplication Left to right Division Addition Left to right Subtraction

A mathematical sentence built from expressions using an equal sign Equation Any and all values of the variables that satisfy an equation, inequality, system of equations, or system of inequalities Solution

Ordered Pair The set of numbers giving the location of a point on a coordinate plane Two numbers written in the form: (x, y) Also known as a point

Example 1: Is the ordered pair a solution to the equation? y = -3x + 5 Pt: (2, -1) y = - 3x + 5 - 1 = - 3(2) + 5 - 1 = - 6 + 5 - 1 = - 1 Yes, the point (2, -1) is a solution to the equation, y = - 3x + 5 x y

Guided Practice 1 Is the following point a solution to the given equation? y = - 2x – 7 Point: (6, -19)

Guided Practice 1 (Poll) Is the following point a solution to the given equation? y = - 2x – 7 Point: (6, -19) A) Yes, it is a solution B) No, it is not a solution

Guided Practice 2 Is the following point a solution to the given equation? y = - 2x – 7 Point: (-4, 1)

Guided Practice 2 (Poll) Is the following point a solution to the given equation? y = - 2x – 7 Point: (-4, 1) A) Yes, it is a solution B) No, it is not a solution

Reflection How do you know if an ordered pair is a solution to an equation? Predict: Assuming the line is linear, where would the solution lie on the graph, if the ordered pair was a solution?

Example 2: Is the ordered pair a solution to the equation? y = -3x + 5 Pt: (3, -5) y = - 3x + 5 - 5 = - 3(3) + 5 - 5 = - 9 + 5 - 5 = - 4 No, the point (3, -5) is not a solution to the equation, y = - 3x + 5 x y

Guided Practice 3 Is the following point a solution to the given equation? y = - 2x – 7 Point: (-2, 6)

Guided Practice 3 (Poll) Is the following point a solution to the given equation? y = - 2x – 7 Point: (-2, 6) A) Yes, it is a solution B) No, it is not a solution

Guided Practice 4 Is the following point a solution to the given equation? y = - 2x – 7 Point: (0, 8)

Guided Practice 4 (Poll) Is the following point a solution to the given equation? y = - 2x – 7 Point: (0, 8) A) Yes, it is a solution B) No, it is not a solution

Reflection How do you know if an ordered pair is not a solution to an equation? Predict: Assuming the line is linear, where would the solution lie on the graph, if the ordered pair was not a solution?

Activity At your table, your group will decide if a point given to you is a solution to the equation: y = 5 – 2x If it is a solution, write true. If it is not a solution, write false. Then, explain your answer to the class and why you chose it as you go up to graph it.

Activity Groups Table 1: Point B: (-5, 4) & Point C: (0, 5) Table 2: Point D: (7, -9) & Point E: (3, -4) Table 3, 4: Point F: (2, 1) & Point G: (7, 6) Table 5: Point H: (1, 3) & Point I: (-9, 7) Table 6: Point J: (3, -1) & Point K: (-2, 7) Table 7: Point L: (0, 0) & Point M: (7, -6) Table 8: Point N: (5, 0) & Point P: (3, 4)

Reflection What do you notice about all the “true” points versus the “false” points?

Quiz Does the given ordered pair satisfy the linear equation? Equation Ordered Pair Yes/No y = 5x (1, 5) y = 2x – 7 (2, -3) y = -11x + 4 (0, 4) y = - x (1, 1)

Homework Things you should be doing right now… Working on your homework Working on your MiMOW Checking your work on the class website Listening to music if you have head phones and no one else can hear your music