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**Warm Ups {(2,0) (-1,3) (2,4)} Write as table Write as graph**

Write as map State domain & range State the inverse

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**5-3 Equations as Relations**

Objective: To determine solutions to equations. Standard 16.0

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**Ordered pairs: always write in alphabetical order**

(x, y) (a, b) (r, s) Linear Equation: an equation that, when graphed, creates a straight line. Solution: ordered pairs that give a true statement

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**Example 1 Which of these are solutions of 3x + y = 8 ?**

Plug in the values for x and y Simplify each side Check if they are equal (4,-4) (8,0) (2,2) (3,1) x y 3(4) + (-4) = 8 = 8 8 = 8 Yes! x y 3(8) + 0 = 8 = 8 24 = 8 No! x y 3(2) + 2 = 8 6 + 2 = 8 8 = 8 Yes! x y 3(3) + 1 = 8 9 + 1 = 8 10 = 8 No!

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**Example 2 Solve the equation 2x + 2y = 14 given x = -3 2(-3) + 2y = 14**

Substitute Solve for remaining variable Write as ordered pair 2x + 2y = 14 2(-3) + 2y = 14 -6 + 2y = 14 2y = 20 y = 10 (-3, 10)

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Given the domain… Solve the equation x + y = 4 if the domain is {-4, -2, 0, 2, 4} Plug it in, domain = x Answer as ordered pairs!

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**What if… I gave you the range instead of the domain?**

How would you solve the equation given the range? Plug the values in for y, then solve for x

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Example 3 Make a table and graph y = x + 6 if the domain is {-4,-3,2,4} This is a linear equation so you should be able to connect the dots and make a line. Answer: (-4,2) (-3,3) (2,8) (4,10)

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**TOO y = -1 for 3x = 13 – 2y x = 10 for 5x + 3 = y Answers (5, -1)**

(10, 53)

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Homework 5-3 Practice

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**Math Lab Warm Ups {(3,-1) (0,4) (2,4) (3,3)} Write as table**

Write as graph Write as map State domain & range State the inverse

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**Practice 1 Solve the linear equation given the following domain:**

2x+ y = 8 domain: {-2, -1, 0, 3, 6}

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**Practice 2 Solve the linear equation given the following range:**

2x+ 4y = 10 range: {-1, 0, 1, 3, 6}

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5.7 Graph Linear Inequalities in Two Variables

5.7 Graph Linear Inequalities in Two Variables

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