Example 11.13 from Prealgebra, 11.1 Use the Rectangular Coordinate System

Use the Rectangular Coordinate System: example 11.13

Find three more solutions to the equation $y .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To find solutions to $3 x + 2 y = 6,$ choose a value for $x$ or $y .$ Remember, we can choose any value we want for $x$ or $y .$ Here we chose $1$ for $x,$ and $0$ and $−3$ for $y .$

Substitute it into the equation.

Simplify.
Solve.

Write the ordered pair. $(2, 0)$ $(1, \frac{3}{2})$ $(4, −3)$

Check your answers.

$3 x + 2 y = 6 .$ $(1, \frac{3}{2})$ $(4, −3)$

So $(2, 0), (1, \frac{3}{2})$ and $(4, −3)$ are all solutions to the equation $3 x + 2 y = 6 .$ In the previous example, we found that $(0, 3)$ is a solution, too. We can list these solutions in a table.

$3 x + 2 y = 6$

$x$ $y$ $(x, y)$

$0$ $3$ $(0, 3)$

$2$ $0$ $(2, 0)$

$1$ $\frac{3}{2}$ $(1, \frac{3}{2})$

$4$ $−3$ $(4, −3)$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find three solutions to the equation: $2 x + 3 y = 6 .$

How did it go?