Use the Rectangular Coordinate System: example 11.12

Find a solution to the equation $3 x + 2 y = 6 .$

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.

Your turn

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

Find a solution to the equation: $4 x + 3 y = 12 .$

How did it go?

Step 1: Choose any value for one of the variables in the equation.		We can substitute any value we want for $x$ or any value for $y .$ Let's pick $x = 0 .$ What is the value of $y$ if $x = 0$ ?
Step 2: Substitute that value into the equation. Solve for the other variable.	Substitute $0$ for $x .$ Simplify. Divide both sides by 2.
Step 3: Write the solution as an ordered pair.	So, when $x = 0, y = 3 .$	This solution is represented by the ordered pair $(0, 3) .$
Step 4: Check.	Is the result a true equation? Yes!

Step 1: Choose any value for one of the variables in the equation.		We can substitute any value we want for $x$ or any value for $y .$ Let's pick $x = 0 .$ What is the value of $y$ if $x = 0$ ?
Step 2: Substitute that value into the equation. Solve for the other variable.	Substitute $0$ for $x .$ Simplify. Divide both sides by 2.
Step 3: Write the solution as an ordered pair.	So, when $x = 0, y = 3 .$	This solution is represented by the ordered pair $(0, 3) .$
Step 4: Check.	Is the result a true equation? Yes!