EDGE Math 8

Linear Equations in x and y

Observe that the set of ordered pairs that satisfy an equation in two variables is a relation. Recall that the domain of a relation is the set of all of its first coordinates and its range is the set of all of its second coordinates.

Example

Identify the domain and range of the set of ordered pairs $(x, y)$ that satisfy each equation.

4 x + 3 y = - 12

y = 3

2 x = - 11

Solution

1.	The set of ordered pairs that satisfy the equation $4 x + 3 y = - 12$ is ${(x, y) \| 4 x + 3 y = - 12} .$ The domain and range of this relation are both equal to the set of all real numbers.
2.	The set of ordered pairs that satisfy the equation $y = 3$ is ${(x, y) \| y = 3} .$ The domain of this relation is the set of all real numbers while its range is ${3} .$
3.	The set of ordered pairs that satisfy the equation $2 x = - 11$ is ${(x, y) \| x = \frac{- 11}{2}} .$ The domain of this relation is ${- \frac{11}{2}}$ while its range is the set of all real numbers.