1. Unit 3: systems of equations and inequalities
Final Exam Review

2. Topics to Include Systems of Equations (2 lines) Line and Quadratic
Line and Circle
Graphing Systems of Equations
Graphing Inequalities
Systems of Inequalities

3. Systems of Equations
To solve a system of equations, you can use one of 2 strategies
SUBSTITUTION
With Substitution, look for ONE VARIABLE that is by itself.
Plug that variable back into the SECOND EQUATION and solve for the other variable.
ELIMINATION
With Elimination, your goal is to get one variable to CANCEL OUT
To do this, transform the system so that the variable you want to cancel is POSITIVE in one equation and NEGATIVE in the other.

4. Systems of Equations
Example of Substitution
Example of Elimination

5. Systems of Equations You Try SUBSTITUTION 𝒚=𝟔𝒙−𝟏𝟏 −𝟐𝒙−𝟑𝒚=−𝟕 You Try
ELIMINATION
𝟓𝒙+𝒚=𝟗
𝟏𝟎𝒙 –𝟕𝒚=−𝟏𝟖

6. Line and Quadratic
Use SUBSTITUTION to solve systems with lines and quadratics
Set both equations EQUAL to each other
FACTOR and Solve. Make sure to plug the x value back in to get the y value.
Example
𝒚= 𝒙 𝟐 +𝟐𝒙+ 𝟒 𝒙 𝟐 +𝟐𝒙+ 𝟒=𝟔𝒙+𝟏
𝒚=𝟔𝒙+𝟏 𝒙 𝟐 −𝟒𝒙+𝟑=𝟎
𝒙−𝟑 𝒙−𝟏 =𝟎
𝒙=𝟑, 𝒙=𝟏
Answers: (3, 19) and (1, 8)

7. Line and Quadratic
You Try
𝒚= 𝒙 𝟐 −𝟒𝒙−𝟓
𝒚= −𝒙−𝟕

8. Line and Circle
Use SUBSTITUTION to solve systems with lines and quadratics
FACTOR and Solve. Make sure to plug the x value back in to get the y value.
Example
𝒙 𝟐 + 𝒚 𝟐 =𝟗𝟖 𝒙 𝟐 + (𝒙) 𝟐 =𝟗𝟖
𝒚=𝒙 𝟐 𝒙 𝟐 =𝟗
𝒙 𝟐 =𝟒𝟗
𝒙=𝟕 𝒂𝒏𝒅−𝟕
Answers: (7, 7) and (-7, -7)

9. Line and Circle
You Try
𝒙 𝟐 + 𝒚 𝟐 =𝟒𝟓
𝒚=𝟐𝒙

10. Graphing Systems of Equations
Besides Substitution and Elimination, you can also GRAPH the 2 equations to solve
Once you graph, the answer is the INTERSECTION of the 2 lines.
Example

11. Graphing Systems of Equations
y= -2x+4
Graphing Systems of Equations
You Try
1. 𝒚=𝟒𝒙+𝟑 2. 𝒚= 𝒙 𝟐 −𝟒𝒙+𝟒 3. 𝒙 𝟐 + 𝒚 𝟐 =𝟗
𝒚= −𝒙−𝟐 𝒚= −𝟐𝒙+𝟒 𝒚= 𝒙+𝟑

12. Graphing Inequalities
When graphing inequalities on a coordinate plane you must pay attention to 2 things
TYPE OF LINE
<𝑜𝑟 > : DOTTED LINE
≤𝑜𝑟 ≥ : SOLID LINE
SHADING
<𝑜𝑟 ≤ : shade BELOW
>𝑜𝑟 ≥ : shade ABOVE

13. Graphing Inequalities
Example:

14. Graphing Inequalities
You try:
𝒚< 𝒙 𝟐 −𝟒𝒙+𝟒 𝒚 ≥ 𝟒𝒙 𝟐 −𝟏

15. Graphing systems of Inequalities
When graphing systems of inequalities, graph BOTH lines on the same graph and SHADE both.
The answer is where BOTH graphs are shaded.
Example

16. Graphing systems of Inequalities
You try:
1. 𝒚 ≤ 𝒙+𝟒 𝒚≥𝒙 𝟐 −𝟓
𝒚< −𝟐𝒙+𝟐 𝒚< −𝒙 𝟐 +𝟏

17. ALL DONE