What the Heck is a Linear Equation Anyway?? |

**What the Heck is a Linear Equation Anyway??**

If you really want to improve your marks in math, pay attention to the words of math. Once you begin learning and using the language of mathematics, you'll begin to see the ever present sense of it. For instance, if you've just learned to write and solve "linear" equations, you should realize that the name is telling you two things. It's telling you that a linear equation has something to do with a line -- hence the "linear" -- and it's also telling you that you're going to see an equal sign since you'll be looking at an equation.

So what the heck is a linear equation anyway??

**A linear equation is an address**. It describes exactly where, in Cartesian space, that line exists. It's almost like your home address. It defines where you live -- so does a linear equation. If we consider the linear equation ** y = 5x + 10**, we can plot a series of points and draw this line. It will cross the

**The ***x*** and ***y*** values of any and every point
on this line satisfy the relation y = 5**

Points off the line will not satisfy this statement.

Thus the line is the set of all points (*x*, *y*) such that the *y*-value is 5 times the *x*-value plus 10.

By the way, all the points in the plane above the line will satisfy the **inequality **** y > 5x + 10**, while the points below the line satisfy

When we have a system of two linear equations, we have an interesting situation. The two equations can be solved algebraically and simultaneously and the result will define the point where the two lines meet when we graph them. Of course, there are **three possibilities**. The lines can meet at **exactly one point**, **no points** because they're parallel, or an **infinite** number of **points** because the two lines are superimposed upon each other. In such a case, one equation will just be a multiple of the other. Let's look at each case.

Say we have ** y = 2x + 3** and

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Now say we consider ** y = 2x + 1** and

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And finally, let's consider ** y = 2x + 3** and

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Don't ignore the words in math. They tell you a lot. After all, **math is just a language** or code that humans developed in order to describe our reality. Learn the words -- you'll learn the math.

**TtT **