1. Chapter 3 Review

2. Systems of Equations Three types of methods to solve. 1.Graphing 2.Substitution 3.Elimination Three types of solutions ◦ One solution ◦ Infinitely many solutions ◦ No solutions

3. Solve using any method. 1) 2x – 3y = 22) x – 0.5y = -3 x + 2y = 15 2x – y = 6 3) 2x + y = 44) 5b = 20 + 2a 3x + y = 8 2a + 4b = 7

4. Campus Rentals rents 2 and 3 bedroom apartments for $700 and $900 per month, respectively. Last month they had six vacant apartments and reported $4600 in lost rent. How many 2 bedroom apartments were vacant?

5. Systems of Inequalities Graph the equation of a line ◦ Write in slope-intercept and graph ◦ Special linear equations Graph the equation of Absolute Value ◦ Write two equations using “or”/ “and” Shading ◦ Shade each inequality individually. Where the shading overlaps is the solution. ◦ If the shading does not overlap then there is no solution.

6. Solve each system of inequalities 1) y ≤ -¾x – 2 2) |x + 1| < 3 y ≥ -¾x + 1 y ≤ -x + 1

7. Vertices of a Polygonal Region To find Vertices of a polygonal region Graph each inequality to determine which equations intersect. Find the point of intersection for each pair of lines using one of the methods of solving systems of equations. Graphing Substitution Elimination Graphing Calculator

8. Find the vertices. 1) y ≤ x y ≥ -3 3y + 5x ≤ 16

9. Systems in Three Variables How to solve three equations. ◦ Determine a variable to eliminate from each equation. ◦ Now use the two new equations you created from step 1 and solve using elimination. ◦ Find all three answers by substituting the numbers back into the previous equations. How can three planes intersect? One point Infinitely many solutions No solution

10. Solve the system of equations. 8x + 12y – 24z = -40 3x – 8y + 12z = 23 2x + 3y – 6z = -10