Jacqueline Martinez Honors Precalculus Period 3 Chapter 7 Systems of Equations and Inequalities

Linear and Nonlinear Systems

100

A set of two or more equations in two or more variables

What is a system of equations

200

Determine which ordered pair is a solution of the system of equations: 

{4x-y = 1

 {6x+y = -6 

(a) (0,-3) (b) (-1,-4) (c) (-3/2, -2) (d) (-1/2, -3)

What is D

300

Solve by method of substitution: 

{2x+y = 6 

{-x+y = 0

What is (2,2)

400

Solve using substitution: 

{-2x+y =-5 

{x² + y² = 25

What is (0,-5), (4,3)

500

Find the sales necessary to break even (R=C) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) 

C = 8650x + 250,000 

R = 9950x

What is 192 units

Two-Variable Linear Systems

100

Two systems of equations that have the same solution set

What is equivalent

200

Solve using elimination: 

{x+3y = 1 

{-x+2y = 4

What is (2,1)

300

Solve using elimination:

 { x -y = 2 

{-2x+2y = 5

What is no solution

400

Solve using any method: 

{3x-5y = 7 

{2x+y = 9

What is (4,1)

500

Find the equilibrium point of the demand and supply equations. The equilibrium point is the price p and the number of units x that satisfy both the demand and supply equations. 

Demand: p = 50-0.5x 

Supply: p = 0.125x

What is (80,10)

Multivariable Linear Systems

100

The process used to write a system of linear equations in row-echelon form

What is Gaussian elimination

200

Determine which ordered triple is a solution of the system of equations. 

{3x -y+ z = 1 

{2x -3z = -14 

{ 5y+2z = 8 

(a) (2,0,-3) (b) (-2,0,8) (c) (0,-1,3) (d) (-1,0,4)

What is D

300

Solve using back substitution. 

{2x-y+5z = 24 

{ y+2z = 6 

{ z = 4

What is (1,-2,4)

400

Perform the row operation and write the equivalent system. Add Equation 1 to Equation 2. 

{ x-2y+3z = 5 

{-x+3y-5z = 4 

{2x -3z = 0

What is {x-2y+3z = 5 { y-2z = 9 {2x -3z = 0

500

Solve the system of linear equations. 

{12x+5y+z = 0 

{23x+4y -z = 0

What is (9a, -35a, 67a)

Partial Fractions

100

If the degree of the numerator of rational expression is greater than or equal to the degree of the denominator, then the fraction is called

What is improper

200

What is the decomposition form of 3x-1/[x(x-4)]?

What is A/x + B/x-4

300

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 7/(x² - 14x)

What is A/x + B/x-14

400

Write the partial fraction decomposition of the improper rational expression. (x² -x)/ (x² +x +1)

What is 1- (2x+1/x^2 +x +1)

500

True or false: For the rational expression x/[(x+10)(x-10)^2] the partial fraction decomposition is of the form A/(x+10) + B/[(x-10)^2].

What is False. The partial faction decomposition is A/(x+10) + B/(x-10) + C/[(x-10)^2]

Systems of Inequalities

100

An ordered pair, (a,b) is a __ of an inequality in x and y if the inequality is true when a and b are substituted for x and y, respectively.

What is solution

200

Graph the inequality. y< 2- x^2

What is (region inside arc is shaded)

300

Use a graphing utility to graph the inequality. Shade the region representing the solution. y< ln x

What is (region below arc is shaded)

400

Determine which ordered pair is a solution of the system of linear inequalities. 

{x >(or = to) -4 

{y >-3 

{y <(or = to) -8x -3 

(a) (0,0) (b) (-1,-3) (c) (-4,0)

What is C

500

Use a graphing utility to graph the systems and find the consumer surplus and the producer surplus.

What is Consumer surplus: $1600 Producer surplus: $400