A system of equations is a set of two or more equations that contain multiple variables.

For example:

$$2x+3y=17\7x+2y=22$$

When given a problem with *n *variables, it will require *n* equations to solve. **The majority of systems of equations questions on the SAT will ask you to solve for two variables using two equations***.*

For two-variable systems, there are three types:

These are the traditional systems. They won’t always tell you there’s one solution, but if you’re simply asked to solve for one of the variables, then it’s this.

Example:

$$y+2x=7\2y+3x=11$$

For the system of equations above, what is the value of *x + y*?

A) 2

B) 3

C) 4

D) 5

**Strategy****:**

**ALWAYS note what you are being asked to solve for (the***x + y*in the example).**Plug both equations into Desmos. Where they intersect is the common solution.**

What one solution looks like on a graph:

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