Systems of Equations What you should be able

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)