Systems of Equations
Does the system of linear equations below have a solution? If so, what is the solution?
-2x+y=6
y-2x=4
a. There is one solution: (1/2, 5)
b. There is one solution: (-1/2,5)
c. There is no solution to the system.
d. The system has infinitely many solutions
c. There is no solution to the system.
Multiply the first equation by -1, and rearrange the second equation. So we have
2x-y=6
-2x+y=4
Add, and we have 0=10. Which is false, so no solutions.
Simplify (x2)3
x6
Lee wants to cut a right triangle out of fabric for a craft project. Which of the following lengths could be the side lengths of the triangle?
a. 8cm, 15cm, 17cm
b. 4cm, 5cm, 6cm
c. 9cm, 40cm, 51cm
d. 1.2cm, 2.4cm, 2.6cm
a. 82+152=172
64+225=289
Mrs. Houck runs at an average speed of 3 miles per hour. Which speed is equivalent to Mrs. Houck's speed?
a. 6 miles in 6 hours
b. 7 miles in 14 hours
c. 9 miles in 3 hours
d. 3 miles in 12 hours
c. 9 miles in 3 hours
Which equation has a solutions that is less than 0?
a. -6m=2(3m-1)
b. 15-(4z+3)=12+z
c. 5(d+2)=3(d-6)
C
5(d+2)=3(d-6)
5d+10=3d-18
2d=-28
d=-14 < 0
The system of equations below has infinitely many solutions.
x-y=8
y-x=c
What is the value of c?
a. -8
b. -1
c. 0
d. 8
a. -8
Evaluate 45/47
1/42=1/16
Nicholas places his 3-foot ladder against a house he is painting. The foot of the ladder is 8 feet from the base of the house. To the nearest tenth of a foot, how high above the ground in the top of the ladder where it touches the house?
a. 4.7 ft
b. 22 ft
c. 28.9 ft
d. 31.0 ft
c. 28.9 ft
Brad earns $15 an hour at his summer job. Which equation compares the amount of money Brad earns, y, to the number of hours he works, x?
a. y=15x+15
b. y=15x
c. y=15+x
d. y=15
b. y=15x
Jamal is shopping for custom sweatshirts for the school soccer team. ShirtCo charges $12.50 per shirt, plus a set-up fee of $16. SportMart charges $14 per shirt, with no set-up fee. Jamal has a coupon for $5 off the total cost at SportMart. Which equation can Jamal use to find the number of shirts, s, for which the total cost is the same for both stores?
a. 12.5s+16=14s-5
b. 12.5(s+16)=14s+5
c. 12.5s-16=14(s-5)
d. 12.5s+16=14(s-5)
a. 12.5s+16=14s-5
In the system of linear equations below, a and b are integers. The solution to the system is (2, -4). Find the values of a and b.
ax+2y=-2
ax+by=10
a. a=3 and b=-1
b. a= 3/2 and b=8
c. a=3 and b=1
d. a=1 and b=-2
NO CALCULATOR!
What is the cube root of -125?
-5
Two lengths of two sides of a triangle are 5 feet and 12 feet. The angle between them is an obtuse angle. What can be said of the length of the third side of the triangle?
a. It is equal to 13 ft.
b. It is greater than 13 ft.
c. It is less than 13 ft.
d. It is between 5 ft and 12 ft.
d. It is between 5ft and 12ft.
Brenda is planting flowers. She can plant 33 flower beds in 3 hours. What is her unit rate?
a. 11 flower beds per hour
b. 10 flower beds per hour
c. 3 flower beds per hour
d. 33 flower beds per hour
a. 11 flower beds per hour
Which equation has no solution?
a. 8y+11=6y+11
b. 10x-1=10x+4
c. 2.1(a+2)=2.1a+4.2
d. 6m+4(m+1)=2(2+m)+7m
b. 10x-1=10x+4
subtract 10x, you are left with -1=4, which is false. No solutions.
Sven solved the system of equations. Each step is labeled.
2x+y=8
3x-y=17
1. 2x+y=8 --> y=8-2x
2. 3x-y=17 --> 3x-8-2x=17
3. x-8=17
4. x=25
In which step does Sven make his first error?
a. 1
b. 2
c. 3
d. 4
b. 2
Correct: 3x-8+2x=17
What is the cube root of 64?
4
A support wire is attached to a utility pole at a point 4 feet below the top of the pole. The wire is anchored to the stake on level ground 10 feet from the base of the pole. If the wire is 26 feet long, how tall is the utility pole?
a. 20 ft
b. 24 ft
c. 28 ft
d. 36 ft
c. 28 ft
Dan is analyzing his reading rate. He says his equation is 3x-2y=0 compares the number of minutes, x, to the number of pages he reads. What is Dan's reading rate as a unit rate?
3x-2y=0
2y=3x
y=(3/2)x
His reading rate is 3/2 pages per minute.
Emma substitutes 3 for x in a one-variable linear equation and finds that it make the equation true. She then substitutes 5 for x in the same linear equation and finds that 5 also makes the equation true. What can you conclude about the number of solutions of the equation?
a. There are no solutions
b. There are exactly two solutions
c. There are exactly two solutions
d. There are infinitely many solutions
d. There are infinitely many solutions
The perimeter of a rectangular garden is 100 feet. The length of the garden is 8 feet longer than twice the width.
Let l=length and w=width. Which system of equations models this situation?
a. lw=100, l=2w+8
b. 2l+2w=100, w=2l+8
c. l+w=100, l=2w+8
d. 2l+2w=100, l=2w+8
d. 2l+2w=100, l=2w+8
Which expression is not equal to 1?
a. 1-1
b. (20)1
c. (3-3)(33)
d. 42/4-2
d. 42/4-2=42-(-2)=44=256
A park is a rectangle that is 80 yards long and 60 yards wide. Two concrete walkways lie on the diagonals of the rectangle. What is the sum of the lengths of the walkways?
a. 100 yards
b. 200 yards
c. 280 yards
d. 480 yards
b. 200 yards
Which equation represents a proportional relationship between x and y in which the unit rate is 5?
a. 5x+5y=0
b. 5x-5y=5
c. 5y+x=5
d. 5x-y=0
d. 5x-y=0
Add y to both sides: y=5x
What is the solution to the equation?
6.1t-2.1(t+2)=3(t+1.5)
a. t=0
b. t=0.3
c. t=6.6
d. t=8.7
d. t=8.7
6.1t-2.1(t+2)=3(t+1.5)
6.1t-2.1t-4.2=3t+4.5
4t-4.2=3t+4.5
t=8.7