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Precalculus
8 - 01 Nonlinear and Linear Systems
System of Equations
- Several equations with the ___________________solution
Substitution
- ___________________one equation for a variable
- ___________________this expression into the other equation
- ___________________the new equation
- ___________________the solution back into the 1 st equation and solve
- ___________________your answers!
Solve {
2
Graphical Method
- ___________________both equations on ___________________coordinate plane
- The points of ___________________are the solutions.
Solve graphically
2
Precalculus
8 - 02 Two-Variable Linear Systems
Three possibilities for solutions
- 1 Solution: ___________________
and _____________________
- Infinitely Many Solutions:
_____________________ and
_____________________
- No Solution: _________________
Solving Linear Equations by Elimination
- Write the equations in _____________________( ax + by = c )
- Obtain coefficients of one variable that differ only in ___________________by _____________________the equations by constants.
- _____________________the equations and _____________________the resulting equation. (A variable will be eliminated.)
- ___________________________ the answer into either original equation and solve.
- _____________________your solution.
- If _____________________the variables are _____________________and the result is
o True (like 0 = 0), there are ____________________________________
o False (like 0 = 9), there are ___________________________________
Solve {
Solve {
Solve {
Precalculus
8 - 04 Partial Fractions
- To split a rational function into smaller ___________________
2
To Find Partial Fractions
- ___________________the denominator.
- For each ___________________factor of the denominator are in the form
2
- For each ___________________factor of the denominator are in the form
2
2
2
- ___________________for A , B , C , etc.
- Multiply by the ___________________
a. Choose ___________________values of x to find A , B , C , etc.
b. Or create a ___________________of linear equations based on the ___________________of x.
Find the partial fractions
𝑥+ 8
𝑥
2
Precalculus
8 - 05 Systems of Inequalities
Solve Systems of Inequalities
- Graph ________________the inequalities on the ________________coordinate plane.
- Find the ________________of the ________________areas.
Graph an Inequality
- Pretend the inequality sign is = and ________________the line.
- Decide if the line is ________________or ________________
a. Solid if ________________
b. Dotted if ________________
3. ________________
a. Pick a ________________point ________________on the line.
b. ________________the test point into the inequality
i. If this results in a ______________statement, then shade the side of the graph ________________the test point.
ii. If the result is _____________a true statement, then shade the ________________side of the graph.
c. OR if solved for ________________
i. y > shade ________________the line.
ii. y < shade ________________the line.
Solve {
Solve {
2
Precalculus
8 - 06 Linear Programming
- _______________________strategy
o _______________________or _______________________
- _______________________function to optimize
- _______________________– system of inequalities
Steps for Linear Programming
- Graph _______________________and find _______________________of solution
- Max or min will be at _______________________
- Plug _______________________into _______________________function to find min or
max
Find the minimum value of 𝑧 = 4 𝑥 + 6 𝑦 subject to
