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WorksheetsAlgebra Review Quiz #4 Systems of Equations/Inequalities
Total questions: 30
Worksheet time: 55mins
What is the solution?
1
-2
(1, 2)
(1, -1)
Many Solutions
This system has _____ solutions
0
1
2
Infinitely many
(-3,-2)
What is the solution?
(Hint: Both lines are graphed over each other)
One Solution
No solution
Infinitely Many Solutions
Two Solutions
Not Enough Information
Solve the following system by graphing. What is the solution?
(-2, -4)
(2, -4)
(-2, 4)
(2, 4)
Infinity Many Solutions
Solve the following system by graphing. What is the solution?
Infinite number of solutions
(3, 3)
(3, -3)
(-3, 3)
No solutions
Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. Which of the following points is NOT a vertex of the shaded region?
(10,2)
(6, 6)
(0,0)
(0,3)
No Solution
A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with corn can be modeled by P=4000x+3000y . What is the maximum profit that she can earn?
$15,000
$21,000
$18,000
$25,000
Their is no solution region therefore there is no maximum profit.
Which of the following represents the situation:
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
1.5x+0.5y=78.5
x+y=87
1.5x+0.5y=78.5
1.5x+0.5y=87
x+y=78.5
1.5x+0.5y=87
x+y=78.5
x+y=87
This is a systems of inequalities so none of the equations are correct.
Which of the following represents the situation:
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.
x+y≤300
7.5x+5.5y≥2000
x+y<300
7.5x+5.5y≥2000
x+y≤300
7.5x+5.5y≤2000
x+y>2000
7.5x+5.5y≤300
This is a systems of equations so none of the inequalities are correct.
Which of the following represents the situation:
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair.
10x+15y≤480
45x+25y≥250
10x+25y≤200
15x+45y≤480
10x+25y>200
15x+45y<480
10x+25y≥200
15x+45y≤480
This is a systems of equations that would be solve most simply by using elimination.
Ron has $1.65 in a collection of only dimes and quarters. Which are possible solutions for the amount of quarters Ron has, check ALL that apply.
1 Quarter
2 Quarters
3 Quarters
5 Quarters
Not enough information
What is the solution to the systems
x+y=5
x-y=3
(8,3)
(5,2)
(6,-1)
(4,1)
No solutions
What is the solution to the systems:
3x+y=11
y=x+3
(4,7)
(0.5,3.5)
(-2,17)
(2,5)
No Solution
What is the solution to the systems:
y=-3x-2
6x+2y=-4
(6,2)
(-1,-5)
(-2,-8)
Infinity Many Solutions
No Solution
Elber bought 11 binders and notebooks from the store and spent $45. Binders cost $6 each and notebooks cost $2.50 each. Which equations would you use to find the numbers of binders, b, and notebooks, n, she purchased
b+n=11
b+n=45
6b+2.5n=11
6b+2.5n=45
2.5b+6n=11
Which ordered pairs are solutions to the inequalities 2x-y>-4 Check all that apply.
(-4,-3)
(1,-6)
(-2,-5)
(8,2)
(-2,0)
Which graph represents the solution to the inequality
x - 4y ≤ -12
The lines on the graph should be dotted so none of the graphs are the correct solution
Which inequality represents the graph?
y≤1/2x-1
y≤3/2x+2
y≥1/2x-1
y>3/2x+2
y<3/2x-1
Which inequality is represented in the graph?
x<-2
x>-2
y<-2
y>-2
Undefined
Which point on the graph in the picture is included in the solution to the following systems of inequalities?
y > 2/3 x+1
5x + 6y < -30
A
B
C
D
None of the points are in the solution region.
Andy says that a systems of two linear equations must have at least one solution as long as the lines have different y intercepts. For example, the equation y=2x+4 and y=4x-6 have different y intercepts and have a solution at (5,14)
Select a pair of linear equations that can be used to disprove Andrea's claim
y=-2/3x+4
y=3/2x-4
y - 2x=4
4y -8x =16
y+4x=1
y+4x=3
y=5/3x+3/5
y=3/5x+5/3
Andy is correct any equations with different y-intercepts have exactly one solution, a coordinate pair.
Which of the following is the graph for the systems of inequalities:
y ≤ -2x + 5
y > 3x - 1
The shaded region should be on the top, so none of the graphs are shaded correctly
If you solve a systems of equations by substitution and your substituted equation is 3y=3y+6, how many solutions does the systems have?
No Solutions
1 Solution
2 Solutions
Infinitely Many Solutions
Not enough information to know
After doing elimination your equation works out to be 0x+0y=0, how many solutions does your systems of equations have?
No Solutions
1 Solution
2 Solutions
Infinitely Many Solutions
Not Enough Information
After doing elimination you get an equation of -5x+0y=-27, how many solutions does your systems of equations have?
No Solutions
1 Solution
2 Solutions
Infinity Many Solutions
Not Enough Information
If a systems of linear inequalities with 2 equations has no solution which of the following must be true? Choose both correct answers!
The Lines are Parallel
The Lines are Perpendicular
Both Lines are Less than y
Both Lines are Greater than y
One Line is Greater than y and One Line is Less than y
There are two types of memberships to the water park in Moses Lake, an unlimited membership cost $70 for the summer, or a summer membership cost $10 plus $5 every visit. How many visit would an individual have to make to make the unlimited membership more cost effective than the summer membership.
The unlimited is always a better deal
10 trips
12 trips
13 trips
The summer membership is always a better deal
Jerry decides he wants to find the solutions of the a systems of equations with a linear are quadratic function. Choose all the solutions of the equation y= -x+2 and y=x2,
(-2,4)
(-1,1)
(0,0)
(1,1)
Infinity Many Solutions
Choose all the coordinate pairs that are a solutions to the systems of inequalities.
(4,0)
(0,4)
The point of intersection of the two lines (1,1)
(0,0)
(8,-8)
