The most important step is to know what a solution would look like.
If there's only one variable in an equation, then the solution is a number.
In this one, however, there are two variables. The solution is any PAIR of
numbers, one for each variable, that make the equation a true statement
when you write the numbers in place of the letters 'x' and 'y'.
You may be dismayed to learn that there are an infinite number of such
solutions. The equation itself can be used to draw a graph. The graph
of this one is a straight line. EVERY POINT on the line has a set of x-y
numbers. Every one of them is a solution to the equation ... and I think
you know how many points there are on a straight line !
Here are a few solutions to the equation.
There are an infinite number more besides these:
x = -2, y = 21
x = -1, y = 18
x = 0, y = 15
x = 1, y = 12
x = 2, y = 9
x = 3, y = 6
x = 4, y = 3
x = 5, y = 0
x = 6, y = -3
x = 7, y = -6
Here's how to make other solutions to it ... as many as you want:
- Pick a number, any number. That'll be the 'x' of the solution.
- Change the sign of the number. If it's positive, make it negative, etc.
- Take what you have and triple it.
- Take what you have and add 15 to it.
- Now you have the 'y' of the solution.
- The 'x' and the 'y' that you have now are another solution to the equation.
On the graph, they're another point on the line.
- You're really chipping away at the list of solutions.
Now there are only another infinite number of them left.
