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+7y=11

*Equation 2:* -3x+2y=7

Notice that both equations have 3x terms (one is positive, the other is negative). You can eliminate the x-terms from the equations if you add the equations. **If the terms you want to eliminate have the opposite sign, you need to add the equations.**

(3x+7y=11)

**+**(-3x+2y=7)

___________

0 + 9y = 18

Notice that 3x + (-3x) = 0. You have now eliminated **x** from the system! It’s easy to solve for **y** now:

9y = 18

y=18/9

**y = 2**

Now put **y=2** into either equation, and solve for **x**:

3x+7y=11

3x+7(2)=11

3x+14=11

3x = 11-14

3x = -3

x = -3/3

**x = -1**

So the two lines intersect at **(-1,2)**. Here’s a graph of what the system looks like:

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