ADVANCED TRIG

Topics• Substitution- Elimination- Cramer’s rule

- Types of systems- Matrices- Function notation

1. Solve the system below using substitution

x = -11 + y7x + 4y = -22

2. Solve the system using elimination

9x – 7y = 510x + 3y = -16

3. Find a, b, c and d within the Cramer’s rule set up below, then solve using determinants

5x – 3y = 226x – 7y = 41

x =

𝜋

4. Inconsistent, dependent, or consistent ?

a. When solving a system if the solution is 0 = 3 what type of system does that indicate?

b. A system with infinite solutions is a ____________ system

c. What type of system gives you are reflexive solution when solving this type algebraically? Such as a solution like 6 = 6.

5. Use your calculator to find the intersection point(s) of the two functions below, type 2nd calc intersect.

f(x) = 3x – 2g(x) = +1Truncate to 3 decimal places. (this means, don’t round) Example: if the solution is x = 3.4678 you write x = 3.467

6. Solve the following systemfind the value for the variable z.

4w + x + 2y – 3z = -16-3w + 3x – y + 4z = 20-w + 2x + 5y + z = -45w + 4x + 3y – z = - 10

7. Function notationIf f(x) = x + 3 and g(x) = Finda. f(2)b. g(f(0))c. f(g(a))d. g(f(x))e. g(4) + f(1)

8. Solve the systemusing any method

9. What type of system is this? (use as many words as possible)

10. Function notationIf and Find the following

a. )

b. f(g(x))

11. Word problemYour overhead costs for your lemonade stand is $500 and it costs you $.08 to make one glass of lemonade. If you sell each glass for $1.75, how many glasses do you have to make to break even?

ANSWERS

1. ANSWERSolve the system below using

substitutionSOLUTION

x = -11 + y7x + 4y = -22

(-6,5)

2. AnswerSolve the system using elimination

9x – 7y = 510x + 3y = -16

(-1, -2)

3. AnswerFind a, b, c and d within the Cramer’s rule

set up below, then solve using determinants

5x – 3y = 226x – 7y = 41

a = 22 b = 41 c = -3 d = -7x = =

4. AnswerInconsistent, dependent, or consistent

a. When solving a system if the solution is 0 = 3 what type of system does that indicate?

parallel

b. A system with infinite solutions is a ____________ system coinciding

c. What type of system gives you are reflexive solution when solving this type algebraically? Such as a solution like 6 = 6. coinciding

5. Answer Use your calculator to find the intersection point(s)

of the two functions below

f(x) = 3x – 2g(x) = +1(-1.302, -5.908) and (2.302, 4.908)

(2nd trace)

6. Solve the following systemfind the value for the variable z. SOLUTION4w + x + 2y – 3z = -16-3w + 3x – y + 4z = 20-w + 2x + 5y + z = -45w + 4x + 3y – z = - 10

Steps: enter the matrix into the calculator, then run rref under matrix, math menu.

(-1, 1, -2, 3) so z = 3.

4 1 2 -3 -16-3 3 -1 4 20-1 2 5 1 -45 4 3 -1 -10

7. Function notationSOLUTIONS

If f(x) = x + 3 and g(x) =

Finda. f(2)= 2 + 3 = 5b. g(f(0))= g(3)=9 – 3 + 1 = 7c. f(g(a))= (d. g(f(x))= e. g(4) + f(1)= 13 + 4 = 17

8. Answer Solve the system using any method

X = -7 Y = -2

9. Answer What type of system is this? (use as many words as possible)

parallel

10. Answers Function notationIf and Find the following

a. = 4 – 6 + 2 = 0b. ) = f(4(0)) = f(0) = 0 – 0 + 2 = 2c. = g((d. = g(4) = 4 x 4 = 16e. f(g(x)) =

11. Answer Word problemYour overhead costs for your lemonade stand is $500 and it costs you $.08 to make one glass of lemonade. If you sell each glass for $1.75, how many glasses do you have to make to break even?

500 + .08x = 1.75x 500 = 1.67x299.40 = x you have sell about 300.