EDGE Math 8

Ordered Pairs

In the previous example, the first coordinate of the ordered pair $(2 + 3, 2 (- 3))$ is equal to 5 and its second coordinate is equal to –6. Hence, $(2 + 3, 2 (- 3)) = (5, - 6) .$

Two ordered pairs are said to be equal if their corresponding coordinates are equal. For example, the ordered pairs $(- 12, 9)$ and $(x, y)$ are equal if $x = - 12$ and $y = 9.$ However, the ordered pair $(8, - 8)$ is not equal to $(- 8, 8) .$

Example

Solve for x and y in each equation.

(x, - 2) = (8, y)

(- 5, - y + 3) = (x + 1, 0)

Solution

1. $x = 8$ and $y = - 2$

2. Solving each of the equations $x + 1 = - 5$ and $- y + 3 = 0$ results in the following:

\begin{array}{l} x + 1 = - 5 \\ x = - 5 - 1 \\ x = - 6 \end{array}

and

\begin{array}{l} - y + 3 = 0 \\ - y = - 3 \\ y = 3. \end{array}