Systems of Equations, where you have more than one equation and are trying to find the intersection between them, can be solved in a number of ways. Here we will look at the Elimination Method, also known as the Addition/Subtraction method.

Let’s look at a simple system of equations:

*Equation 1:* 3x+5y=12

*Equation 2:* 7x+5y=8

Notice that both equations have 5y terms. You can eliminate the y-terms from the equations if you add or subtract the equations. **If the terms you want to eliminate have the same sign, you need to subtract the equations.**

(3x+5y=12)

**–**(7x+5y=8)

___________

-4x + 0 = 4

Notice that 5y – 5y = 0. You have now eliminated **y** from the system! It’s easy to solve for **x** now:

-4x = 4

x = 4/-4

**x = -1**

Now put x=-1 into either equation, and solve for y:

3x +5y = 12

3(-1) +5y = 12

-3 + 5y = 12

5y = 12+3

5y = 15

y = 15/5

**y = 3**

So the two lines intersect at **(-1,3)**. Here’s a graph of what the system looks like:

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