Unit 3: Systems of Equations and Inequalities

Foundations of Math 2 Final Exam Review Name: ______

UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

Part 1: Systems of Equations

v  To solve a system of equations, you can use one of 2 strategies

v  ______

v  With Substitution, look for ______ that is by itself.

v  Plug that variable back into the ______ and solve for the other variable.

v  ______

v  With Elimination, your goal is to get one variable to ______

v  To do this, transform the system so that the variable you want to cancel is ______in one equation and ______in the other.

v  You Try You Try

v  SUBSTITUTION ELIMINATION

  y=6x-11 5x+y=9

  -2x-3y=-7 10x–7y=-18

______

Part 2: Line and Quadratic

v  Use ______ to solve systems with lines and quadratics

v  Set both equations ______to each other

v  ______and Solve. Make sure to plug the x value back in to get the y value.

v  You Try

  y=x2-4x-5

  y=-x-7

Unit 3: Line and Circle

v  Use ______to solve systems with lines and quadratics

v  ______and Solve. Make sure to plug the x value back in to get the y value.

v  You Try

  x2+y2=45

y=2x

______

Unit 4: Graphing Systems of Equations

v  Besides Substitution and Elimination, you can also ______the 2 equations to solve

v  Once you graph, the answer is the ______of the 2 lines.

v  You Try

1. y=4x+3 2. y=x2-4x+4 3. x2+y2=9

y=-x-2 y=-2x+4 y=x+3

______

Part 5: Graphing Inequalities

v  When graphing inequalities on a coordinate plane you must pay attention to 2 things

v  ______

v  <or : ______

v  ≤or≥ : ______

v  ______

v  <or≤ : shade ______

v  >or≥ : shade ______

v  You try:

1.  y<x2-4x+4 2. y≥4x2-1

______

Part 6: Graphing Systems of Inequalities

v  When graphing systems of inequalities, graph ______lines on the same graph and ______both.

v  The answer is where ______graphs are shaded.

v  You try:

1. y≤x+4 2.y≥x2-5

y<-2x+2 y<-x2+1

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