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Intro to Systems of Equations

Systems of Equations deals with more than one equation. At first, you will usually be seeing two equations. If you are asked to solve the system, you are being asked to find the point(s) of intersection between the two graphs.

For example, let’s look at two lines:

Equation 1: y=3x-2
Equation 2: y=-4x+5

Recall the equation of a line, y=mx+b, where m is the slope and b is the y-intercept.

Let’s graph the two lines. The blue line is Equation 1, y=3x-2, and the purple line is Equation 2, y=-4x+5.

If you graphed the lines accurately, it should be pretty easy to see that they cross at the point (1,2). Congrats, you just solved the system of equations by graphing! This method is perfectly fine, but it is a bit time consuming.

Next you should figure out how to solve a system just by using algebra. It’s much quicker.