Name: _______________________________________ Outcome 3 Final Exam Review Practice Multiple Choice
1. If there is one solution to a system of two linear equations, then the graph of the equation is:
a.
b.
c.
d.
The same line
Two intersecting lines
Two parallel lines
Two perpendicular lines
2. Solve the system of equations using the method of your choice:
{
−𝟏𝟓𝒙 + 𝟔𝒚 = −𝟏𝟐
𝟏𝟒𝒙 − 𝟔𝒚 = 𝟏𝟎
a.
b.
c.
d.
(-2,-7)
(3,2)
(-2,7)
(2,3)
3. Which of the following shows the solution for the system of linear equations?
y = 3x – 4
B.
A.
C.
D.
4. Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the
next day and buys three shirts and five pairs of pants for $115.00. Write a system of equations to represent this
situation if x represents the number of pairs of pants and y represents the number of shirts.
𝟒𝒙 + 𝟑𝒚 = 𝟖𝟓. 𝟓𝟎
a. {
𝟑𝒙 + 𝟓𝒚 = 𝟏𝟏𝟓. 𝟎𝟎
𝒙 + 𝒚 = 𝟖𝟓. 𝟓𝟎
b. {
𝟑𝒙 + 𝟓𝒚 = 𝟏𝟏𝟓. 𝟎𝟎
𝟑𝒙 + 𝟒𝒚 = 𝟖𝟓. 𝟓𝟎
𝟓𝒙 + 𝟑𝒚 = 𝟏𝟏𝟓. 𝟎𝟎
c. {
5. A system of two linear equations is graphed. The lines have the same slope, but different intercepts. How
many solutions does the system have?
A.
B.
C.
D.
0 The lines would be parallel
1
2
Infinitely Many
6. What is the solution for the system of linear equations shown?
A. x = 2
B. (3, 2)
C. x = 3
D. (2, 3)
7. The graph of a system of two linear equations has no solution. What is true about the lines?
A.
The lines are perpendicular.
B.
The lines have the same slope, but different intercepts.
C.
The lines have the same intercept, but different slopes.
D.
The lines are on top of each other.
8. What is the system of linear equations graphed below? B
9.
10. The solution for a system of two linear equations is (0, 0). Which equation below could be one of the
equations in the system?
A.
B.
y = –3x
C.
y = 4x – 5
D.
y=5–x
11. Is (0, 3) a solution to the following system?
A.
No, because it does not check in either equation.
B.
No, because it does not check in the first equation.
C.
No, because it does not check in the second equation.
D.
Yes, because it checks in both equations.
12. A wholesaler is offering two different packages of custom printed T-shirts and sweatshirts to groups for fundraisers. One package contains 10 dozen T-shirts and 14 dozen sweatshirts for $1544. The other package contains
18 dozen T-shirts and 8 dozen sweatshirts for $1472. Write and solve a system of linear equations to find the
cost, in dollars, of a dozen T-shirts.
a.
$76
c. $48
b.
$58
d. $36
13. Which of the following would be the best first step to solve the system of equations?
2x – 9y = 6
4x – 3y = –7
A.
Subtract the two equations.
B.
Add the two equations.
C.
Solve for y.
D.
Multiply the first equation by -2.
14.
Which of the following points is a solution to the system of inequalities graphed below?
A.
(2, 0)
B.
(–1, 0)
C.
(2, 1)
D.
(–3, 2)
15. Graphically, a point is a solution to a system of two inequalities if and only if __________.
A.the point lies in the shaded region of the first inequality, but not in the shaded region of the
second inequality
B. the point lies in the shaded region of the second inequality, but not in the shaded region of the
first inequality
C. the point lies in the shaded regions of both inequalities
D.the point does not lie in the shaded regions of either inequalities
16. Which of the following graphs is the best representation of the system of inequalities below? B
17. Which of the following statements best explains why the point (2, –2) is not a solution to the system of
inequalities graphed below?
A.
The point (2, –2) satisfies the red inequality but not the blue inequality.
B.
The point (2, –2) satisfies the blue inequality but not the red inequality.
C.
The point (2, –2) doesn’t satisfy either the red or the blue inequalities.
D.
The point (2, –2) satisfies both the red and the blue inequalities.
18. Choose the system of linear inequalities that represent the given scenario. Let a represent the number of
adult tickets and let c represent the number of children tickets. There were up to 1,200 tickets available for
the spring carnival. Adult tickets cost $6.00 and children’s tickets cost $3.50. How many tickets of each could
be sold to make at least $6,450? A
A.
B.
C.
D.
19.
The solution to a system of inequalities is __________.
A. a single point that satisfies all inequalities in the system
B. a collection of points that satisfy all inequalities in the system
C. a single point that satisfies at least one inequality in the system
D. a collection of points that satisfy at least one inequality in the system