Unit 19: Systems of Linear Equations

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 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:

One Solution

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:

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

What one solution looks like on a graph: