Unit 7: Systems of Equations

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Presentation transcript:

Unit 7: Systems of Equations Last unit of the year!!!

What is a System of Equations? A System of equations is a set of two or more equations that contain two or more variables. Example 1: 3x + 4 = 12 y = 4x -5 Example 2: Casey orders 3 pizzas and 2 orders of breadsticks for a total of $29.50. Rachel orders 2 pizzas and 3 orders of breadsticks for a total of $23. How much does a pizza cost?

We want to find out what the solution is, if there even is one. Now that we know what a system is, what exactly does it mean to “solve” a system of equations? We want to find out what the solution is, if there even is one.

Ok, so what is a solution of a system of equations? The solution of a system of equations is where, if you are to graph the equations, they 'meet' or intersect. The solution is written as an ordered pair (x,y).

How many solutions can there be to a system of equations?

There are 3 Ways to solve systems of equations… GRAPHING SUBSTITUTION ELIMINATION

Steps to solving systems by Graphing: 1. Put both equations into slope intercept form 2. Graph both equations 3. Find the intersection (if there is one) of the two lines and state the coordinate (x,y)

3x + y = 5 y – x = 1

x + y = 4 2y – x = 2

3x + y = −2 6x + 2y = −4