2-Variable Equations

We’ve learned how to solve mathematical expressions and mathematical equations with one variable.  How then, do we go about solving equations with two variables?  The answer is that we can’t, unless we specify a value for one of the variables, usually the “input” variable, x.  The reason goes beyond the scope of this subset, but basically, in order to solve for n number of variables, you need n number of unique equations to solve for them.  With only one equation, a 2-variable equation can’t be solved, unless if one of the variables is specified or “inputted”.  For example, in the following equation: 

y = 2x 

There is no way to solve for both y and x with only this equation.  Instead, we must first give one of the variables a value and then solve for the other variable afterwards.  For instance, if we let x = 2, then y = 4.  We can solve for specific cases of the equation this way.  If we keep on solving for specific cases of the equation this way, we will see a trend in the data and can graph it.

The line graph is a powerful tool for visualizing 2-variable equations, because it visually tells us what the value pairs of the two variables, x and y, must be.  If x = 3, then y = 6, and if x = 4, then y = 8, etc.  The specific points that are found on the line’s graph, are called ordered pairs, (x,y).