Module 11.1 Solving Systems Of Linear Equations By ...

Module 11.1 ? Solving Systems Of Linear Equations ? By Graphing

P. 480

+ = is a linear equation. It has an infinite number of solutions; meaning there are an infinitely many numbers that can be substituted for x and y, in order that they satisfy the equation. For example, here are just a few:

y-intercept

x-intercept

Here is a graph of this equation.

ALL POINTS ON THE LINE SATISFY THE EQUATION.

- + = is also a linear equation. It too has an infinite number of solutions. For example, here are just a few:

y-intercept

x-intercept

Here is a graph of this equation.

When we say a System of Linear Equations, we mean two or more linear equations. The two previous examples are + = and - + = Here they are, graphed individually, then combined:

+ =

- + =

- + =

+ =

Combined

If any point is on both graphs, then it's a solution of both equations. In other words, a solution of a System of Linear Equations is any ordered pair that satisfies all of the equations in the system. It does that at the point where the lines intersect each other.

And since here they intersect at only one point, there is only one solution: The ordered pair appears to be (1 , 4).

What we're doing here is called Solving Linear Systems By Graphing.

- + =

+ =

Yes, it appeared to be (1 , 4). But is that really correct?

You can determine that by using Algebra. Substitute = and = into both equations, and seeing if those two numbers satisfy both.

- + = - + = True

- + =

+ = + = True

They do!

+ =

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