Systems of Equations

What you should be able to answer after learning about systems of equations….. A gym membership at one gym costs $10 every month plus a one-time membership fee of $15, and a gym membership at a another gym costs $4 every month plus a one-time $40 membership fee. After about how many months will the gym membership cost the same amount?

Definitions A System of Linear Equations consists of two or more linear equations that have the same variables. A Solution of a System of Linear Equations is any order pair that satisfies all the equations. A Consistent System has at least one solution. An Independent System has exactly one solution. A Dependent System has infinitely many solutions. An Inconsistent System has no solution.

Special Cases One Point of intersection. One solution Consistent Independent Different Slope

The same line Infinitely many solutions Consistent Dependent Coincident Lines Same slope Same Intercept

Parellel Lines No Intersection No Solution Inconsistent Same slope Different Y-Intercept

Steps to find solution Change both equations to slope intercept form (if needed) Graph the lines using the y-intercept and slope. Y = mx + b m = slope b = y – intercept (starting point)