Systems of Equations Study Guide
Algebra I
Name: ______________________________________
Date: _________________________________
Choose the correct answer for each question.
1.
Solve the system:
x - y = -8
x + 3y = 12
a.
2.
(-5,3)
b. (7, 1)
c. (6,2)
d. (-3, 5)
c. (0,3)
d. (4, 4)
Solve the system:
-x +4y = 12
5x - 2y = -6
a.
3.
(-12,0)
b. (8, 5)
Solve the system:
-3x + y = -7
2x - 5y = 22
a.
4.
(0,-7)
b. (0, -4.5)
c. No solution
d. (1, -4)
c. (2, 1)
d. No solution
Solve the system:
3x + 2y = 8
2x +3y = 7
a. (3,-0.5)
4.
b. (4, -2)
Solve the system:
y = 6x - 1
y=x+4
a.
5.
b. (1, 6)
c. (2,5)
d. (4, 11)
If the graph of a system shows two parallel lines, then:
a.
b.
c.
d.
6.
(1,5)
there are infinite solutions
there is no solution
there may be a solution if the lines are extended
something is incorrect with the graph
What point is the intersection of the graphs of the lines 3x + y = 6 and
-3x + y = -6?
a.
(2,1)
b. (0, 2)
c. (2, 0)
d. (3, 3)
7.
What is true of the graphs of the two lines x = 2y - 6 and x = -3y – 14?
a.
b.
8.
c.
d.
Intersect at (4,2)
One solution
What is true of the graphs of the two lines 3x + 4y = 2 and 9x + 12y = 6?
a.
b.
9.
No solution
Intersect at (2,4)
No solution
Intersect at (0,.5)
c.
d.
Intersect at (0,0)
Infinitely many solutions
What is true of the graphs of the two lines 3x + 5y = -9 and -6x - 10y = -12?
a.
b.
No solution
Intersect at (-3,0)
c.
d.
Intersect at (2,-5)
Infinitely many solutions
c.
d.
-3
4
10. To solve 4x + 2y = 10 and x + y = 4 by elimination,
a.
b.
c.
d.
first multiply the second equation by -2
first multiply the second equation by -1
first multiply the second equation by 2
first multiply the second equation by 4
11. Bob wants to sub 3x + y = 13 into 4x + 3y = 6, he needs to
a. convert the equation to 3x = 13 – y
b. convert the equation x=13-y
c. convert the equation to y= 13 – 3x
d. convert the equation to x = -y-13
12. What is the value of y in the following system of equations?
x + 5y = 7
x - 3y = –1
a.
b.
1
2
13. What is the value of the y-coordinate of the solution to the
system of equations - 3 x + y = 9 and x − y = 7?
a.
6
c.
3
b.
2
d.
-15
14. F i v e times as many girls as boys went to the dance. If a total
of 120 students went to the dance , how many were g i r l s ?
a.
60
c.
100
b.
80
d.
110
15. Which graph represents the following system of inequalities?
-x + y > - 1
2x + y ≥ 2
a.
b.
c.
16. Which of these points is a solution of the system y >- 2x + 3 and -x + y > 0?
a. (2, -6)
b. (-1, -2)
c. (5, 2)
d. (1, 3)
17. Which coordinate point is in the solution set for the system of inequalities shown in the
accompanying graph?
a.
(1,3)
b.
(-1,3)
c.
(1,–5)
d.
(-3,0)
Short Constructed Response – Write the correct answer for each question.
17. Sketch a graph of a system that has infinitely many solutions.
18. Sketch a graph of a system that has no solution.
.
19. The e l e m e n t a r y s c h o o l s t u d e n t s a r e p u t t i n g o n a p l a y
as a fundraiser. The student tickets cost $2.00 each
and the adult tickets cost $4 each. They sold 5 times
as many student tickets as adult tickets. They made
$140. How many student and adult tickets were s old?
20. Write the system of inequalities graphed below:
Extended Constructed Response - Solve the problem (on an extra sheet of paper), showing all work.
21. Telephone company A charges $20 per month and $0.10 per text. Telephone company B charges $15 per
month and $0.20 per text. Let t = the number of texts and C = cost.
a. Write an equation to represent the cost of each plan.
b. Solve the system by graphing.
c. Explain what the solution to the system means in terms of what telephone company to provide
services.