Now that we’ve looked at single variable equations, we’re going to move on to two variable equations. The first type of two variable equation that we’re going to look at is the linear equation.

Now, linear equation is an equation in two variables where each variable is raised to no more than the first power, so there are no squared terms or cubed terms and no square roots.

Next Lesson: System of Linear Equations

The following transcript is provided for your convenience.

And also, the variables are not multiplied by each other. So, for two variables are x and y, there’s no x squared, y squared, and there’s no x times y term. So, one example of linear equation might be 2x+8y = 16.

One of the major differences between two variable equations and one variable equations is that we cannot solve for exact values, or any values, for that matter, for x and y with just one equation. We can solve for x in terms of y, or for y in terms of x, but we can’t get numerical values for both variables. But, solving for one of the variables in terms of the other is going to be sufficient for many applications, so that’s what we’re going to look at here.

First, let’s solve this equation for x. The first step in doing that is going to be to divide each term by 2, so we’re going to be left with x+4y = 8. And so, to further isolate x, we’re going to need to subtract 4y from both sides, and that will leave us with x = 8-4y. You’ll notice we’ve isolated x, but we don’t have a numerical value over here, we just have an expression with a y term in it. So, we can not determine the value of x without knowing the value of y.

That’s the situation we’re in, but that’s the solution to this equation for x in terms of y. Now, let’s solve y in terms of x. We’re going to divide each term in the equation by 8 to get y all by itself. 2x/8 is going to be x/4, plus y, equals 2. We want to isolate y a little further, so we’re going to subtract x/4 from both sides, and that will give us y = 2-x/4. This is the formulation of the equation where it’s solved for y in terms of x, and this is as far as we can get with a single linear equation, but there’s a great deal we can do with these forms of the equations.

Next Lesson: System of Linear Equations