Systems of Linear Equations
Functions and Intervals
Solving Linear Equations and Inequalities
Solving Linear Equations and Inequalities #2
Transversals
100
The cost of renting a canoe to use on River Y costs $31. The cost of renting a canoe to use on River Z costs $4 per hour plus a $11 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers. Write the system of equations to represent the situation.
River Y c=31
River Z c=4n+11
100
Two linear functions are shown. Which function has the greater initial value?
Function A.
100
Solve for x.
-0.48x + 0.28x = 5.4
x = -27
100
A contractor bought 12ft^2 of sheet metal. She has used 2.1 ft^2 so far and has $189 worth of sheet metal remaining. The equation 12.6x - 2.1x = 189 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
$18
100
Streets A and B run parallel to each other. The measure of angle 3 is 148 degrees. The measure of angle 4 is 32 degrees. Find the measure of angle 5.
32 degrees
200
Determine the solution of the system of equations. Explain.
x+3y=0
18y=-6x
Infinite Solutions because the lines are the same.
200
Tell whether each function is linear or nonlinear.
Function A is Nonlinear Functions B is Linear
200
Find the value of x when 6 - 2x = 6x - 10x + 16
x = 5
200
Solve
5/4x +1/3x = 2 1/3 +7/3x
x = -7
200
Using alternate interior angles, write an equation in terms of x that will make line m parallel to line n.
4x + 10 = 78
300
The cost of making copies at Store W is $7 regardless of the number of copies. The cost of making copies at Store Z is 60cents per copy plus a $1 charge for the use of the machine. The total cost, c, of making n copies at either store can be represented by an equation. Write a system to find how many copies you have to make for the cost to be the same at both stores.
c=7
c=0.60n+1
300
On which intervals is the function increasing?
1, 3, 6
300
Use the Distributive Property to solve the equation below.
42 - (3c + 4) = 2 (c+7) + c
c = 4
300
Use the Distributive Property to solve the equation below.
4(x-6)+8=6x-2
x= -7
300
Find the value of x for which r || s. Then find angle 1 and angle 2.
/_ 1 =(65-x)
/_ 2 =(76-2x)
x = 11
/_1=54 and /_2=54
400
What is the solution to the system of equations?
(-4,-5)
400
Graph a function where interval (1) is an increasing interval, interval (2) is a decreasing interval, interval (3) is a constant interval, and interval (4) is a decreasing interval.
400
Solve and determine how many solutions
2(4x+3) = 12x+3-4x+3
Infinite Solutions
400
Solve and determine how many solutions.
32x + 1368x - 68 = 35(40x+88)
No Solutions.
400
In the figure, w||x. Which angles are alternate interior angles?
/_i and /_l
/_k and /_j
500
How many solutions does this system of equations have?
y=2/3x+1
y=4/3x-1
One solution
500
When a new laptop became available in a store, the number sold in the first two weeks was high. Sales decreased over the next week and then they increased slightly over the next week. The following two weeks, the total number sold by the store remained steady. Sketch the graph of this function over the six weeks.
500
A restaurant manager needs to rope off a rectangular section for a private party. The length of the section must be 5.6 m. The manager can use no more than 20 m of rope. Write the inequality you could use to find the possible widths of the roped off section.
11.2 + 2W <=20
500
Write the inequality from the description below. 5/7 times a number minus 9.7 is no more than 12.3
5/7n -9.7 <= 12.3
500
On a recent math test a teacher asked for the measure of /_u . In the figure, p||q. Helena incorrectly said that the measure was 79 degrees. Find the measure of /_u .Then decide which error Helena might have made.
Helena thought that u and t are corresponding, when actually u and t are corresponding and have the same measure.
/_u=101