Systems of Equations
Word Problems
100
1) A graph of the system is shown. What is the solution of the system?
A. (3, -1)
B. (-3, 1)
C. (1, 3)
D. (-3, -1)
B. (-3, 1)
100
2) Two equations are given.
y=-7x+42
4x+2y=24
Which ordered pair will satisfy both equations?
A) (6, 24)
B) (6, 0)
C) (2, 24)
D) (0, 6)
B) (6, 0)
200
6) If a solution to a linear system of equations has infinitely many solutions then what must be true about the graph of the system?
A. The lines are parallel
B. The lines intersect only at one point.
C. The lines coincide or the same.
D. The lines are perpendicular.
C. The lines coincide or the same.
200
3) A system of equations is shown.
3x+5y=42
7x-2y=16
What is the x - value of the solution to the system of equations?
A) 8
B) 6
C) 4
D) -4
C ) 4
300
5) Which is NOT a valid strategy to use when solving the system of equations given below.
12x-4y=12
3x+8y=-4
A. Multiply the first equation by 2 and the second equation by 4.
B. Multiply the first equation by 4 and the second equation by 2.
C. Multiply the second equation by 4.
D. Multiply the first equation by 2.
A. Multiply the first equation by 2 and the second equation by 4.
300
4) At a store, 5 shirts and 3 pairs of shoes cost $500. Each shirt costs the same amount, and each pair of shoes cost the same amount, but each shirt costs $100 less than a pair of shoes.
Which system of equations can be used to find the cost of each shirt x, and each pair of shoes, y?
A) 5x+3y=500
x-100=y
B) 3x+5y=500
x-100=y
C) 3x+5y=500
x=y-100
D) 5x+3y=500
x= y -100
D) 5x + 3y = 500
x = y - 100
400
8) Consider the system of equations shown.
6x-4y=40
x=-y
Which point represents the solution to the system of equations?
A) (4, -4)
B) (-8, 8)
C) (-4, 4)
D) (8, -8)
A) (4, -4)
400
7) Jared and Arthur began saving money the same week. The table shows the models for the amount of money Jared and Arthur have saved after x weeks.
Jared’s saving s = f(x) = 20x + 10
Arthur’s savings = g(x) = 10x + 30
Jared and Arthhur will have the same amount of money saved after ____________weeks.
2 weeks
500
11) A chemist has two solutions; one is 25% acid, and the other is 50% acid. How much of each solution should he mix to produce 250 mL of a solution that is 30% acid?
200 ml of 25 % acid
50 ml of 50% acid
500
12) A phone company charges a monthly fee of $15 plus 15 cents per text message. Another company charges $25 each month plus $10 cents per text message for the same plan.
How many text messages will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone from the second company?
200 text messages