Study Guide: Section 5-3

Equations as Relations

An equation in two variables describes a relation. It is often easier to determine the solution of such an equation by solving for one of the variables.

Example: Solve 3y + 2x = 10 if the domain is {−7, −1, 8}

First solve for y in terms of x:

3y + 2x = 10
3y = 10 − 2x
y = 10 − 2x
3

Then substitute values for x from the given domain:

x y = 10 − 2x
3		 y (x, y)
−7 y = 10 − 2(−7)
3		 8 (−7, 8)
−1 y = 10 − 2(−1)
3		 4 (−1, 4)
8 y = 10 − 2(8)
3		 −2 (8, −2)

Part 1: Solutions to Equations

Directions: Which ordered pairs are solutions of each equation?

1. y = 3x + 1
a. (0, 1)
b. (1/3, 2)
c. (−1, −2/3)
d. (−1, −2)

Answers: a, b, d

2. 2a = 5 − b
a. (5, 0)
b. (5, −5)
c. (5/2, 0)
d. (1, 3)

Answers: b, c

Part 2: Solving Equations for a Given Domain

Directions: Solve each equation if the domain is {−4, −2, 0, 2, 4}.

3. x + y = 4

{(−4, 8), (−2, 6), (0, 4), (2, 2), (4, 0)}

4. y = −4x − 6

{(−4, 10), (−2, 2), (0, −6), (2, −14), (4, −22)}

5. 5a − 3b = 15

{(−4, −35/3), (−2, −25/3), (0, −5), (2, −5/3), (4, 5/3)}

6. 3x − 5y = 8

{(−4, −4), (−2, −14/5), (0, −8/5), (2, −2/5), (4, −4/5)}

7. 6x + 3y = 18

{(−4, 14), (−2, 10), (0, 6), (2, 2), (4, −2)}

8. 4x + 8 = 6y

{(−4, −4/3), (−2, 0), (0, 4/3), (2, 8/3), (4, 4)}