MAT 202 Final Exam College Algebra Questions And Answers
2026/2027 Jersey College
Q1. Solve the system x + y=10and x− y =2.
A) ( 6,4 )
B) ( 4,6 )
C) ( 8,2 )
D) ( 5,5 )
Correct Answer: A) ( 6,4 )
Rationale: Adding the equations gives 2 x=12, so x=6 . Substituting into
x + y=10gives y=4 .
Q2. Solve the system 2 x+ y =7and x− y =2.
A) ( 2,3 )
B) ( 3,1 )
C) ( 1,5 )
D) ( 4 ,−1 )
Correct Answer: B) ( 3,1 )
Rationale: Adding the equations eliminates y : 3 x=9 , so x=3 . Then 3− y=2,
giving y=1 .
Q3. Find the intersection of y=2 x +1and y=−x+7 .
A) ( 1,3 )
B) ( 3,4 )
C) ( 2,5 )
D) ( 4,3 )
Correct Answer: C) ( 2,5 )
Rationale: Set the expressions for y equal: 2 x+1=−x+ 7. Thus 3 x=6 , so x=2
and y=5 .
Q4. How many solutions does the system 2 x+ 4 y=8and x +2 y =7have?
A) Exactly one
B) Exactly two
C) Infinitely many
D) No solution
Correct Answer: D) No solution
,Rationale: Dividing the first equation by 2 gives x +2 y =4 , which has the
same left side but a different constant from x +2 y =7. The lines are parallel.
Q5. What is true of the system x + y=3 and 2 x+2 y=6?
A) It has infinitely many solutions
B) It has no solution
C) Its only solution is ( 1,2 )
D) Its only solution is ( 2,1 )
Correct Answer: A) It has infinitely many solutions
Rationale: The second equation is exactly twice the first, so both equations
represent the same line.
Q6. Solve 3 x+ 2 y =12and y=x .
A) ( 2,2 )
B) ( 12 12
5 5
, )
C) ( 3,3 )
D) ( 5 5
12 12
, )
Correct Answer: B) ( 125 , 125 )
12
Rationale: Substitute y=x : 3 x+ 2 x=12 , so 5 x=12and x= y = .
5
Q7. Solve the system x +2 y =8and 3 x−2 y=8 .
A) ( 3,2 )
B) ( 2,3 )
C) ( 4,2 )
D) ( 4,4 )
Correct Answer: C) ( 4,2 )
Rationale: Adding the equations gives 4 x=16, so x=4. Substitution into
x +2 y =8gives y=2.
Q8. A theater sells adult tickets for $12 and child tickets for $8. If 20
tickets generate $200, how many of each type were sold?
, A) 15 adult and 5 child
B) 5 adult and 15 child
C) 12 adult and 8 child
D) 10 adult and 10 child
Correct Answer: D) 10 adult and 10 child
Rationale: Let a+ c=20and 12 a+8 c=200. Substitution gives a=10 and c=10 .
Q9. Which description represents the graph of y >2 x−1?
A) A dashed line y=2 x−1with the region above the line shaded
B) A solid line y=2 x−1with the region below shaded
C) A dashed line y=−2 x +1with the region above shaded
D) A solid line y=−2 x +1with the region below shaded
Correct Answer: A) A dashed line y=2 x−1with the region above the line
shaded
Rationale: A strict inequality uses a dashed boundary, and y >¿indicates
points above the boundary line.
Q10. Which point satisfies both x + y ≤ 6 and x ≥ 2?
A) ( 1,2 )
B) ( 3,2 )
C) ( 5,3 )
D) (−, 24 )
Correct Answer: B) ( 3,2 )
Rationale: For ( 3,2 ) , 3+2=5≤ 6 and 3 ≥ 2.
Q11. A store sells 30 pens consisting of $3 pens and $5 pens. Total
sales are $120. How many $5 pens were sold?
A) 10
B) 12
C) 15
D) 20
Correct Answer: C) 15
Rationale: Let x + y=30and 3 x+ 5 y =120. Subtracting 3 x+ 3 y =90gives 2 y=30 , so
y=15 .
2026/2027 Jersey College
Q1. Solve the system x + y=10and x− y =2.
A) ( 6,4 )
B) ( 4,6 )
C) ( 8,2 )
D) ( 5,5 )
Correct Answer: A) ( 6,4 )
Rationale: Adding the equations gives 2 x=12, so x=6 . Substituting into
x + y=10gives y=4 .
Q2. Solve the system 2 x+ y =7and x− y =2.
A) ( 2,3 )
B) ( 3,1 )
C) ( 1,5 )
D) ( 4 ,−1 )
Correct Answer: B) ( 3,1 )
Rationale: Adding the equations eliminates y : 3 x=9 , so x=3 . Then 3− y=2,
giving y=1 .
Q3. Find the intersection of y=2 x +1and y=−x+7 .
A) ( 1,3 )
B) ( 3,4 )
C) ( 2,5 )
D) ( 4,3 )
Correct Answer: C) ( 2,5 )
Rationale: Set the expressions for y equal: 2 x+1=−x+ 7. Thus 3 x=6 , so x=2
and y=5 .
Q4. How many solutions does the system 2 x+ 4 y=8and x +2 y =7have?
A) Exactly one
B) Exactly two
C) Infinitely many
D) No solution
Correct Answer: D) No solution
,Rationale: Dividing the first equation by 2 gives x +2 y =4 , which has the
same left side but a different constant from x +2 y =7. The lines are parallel.
Q5. What is true of the system x + y=3 and 2 x+2 y=6?
A) It has infinitely many solutions
B) It has no solution
C) Its only solution is ( 1,2 )
D) Its only solution is ( 2,1 )
Correct Answer: A) It has infinitely many solutions
Rationale: The second equation is exactly twice the first, so both equations
represent the same line.
Q6. Solve 3 x+ 2 y =12and y=x .
A) ( 2,2 )
B) ( 12 12
5 5
, )
C) ( 3,3 )
D) ( 5 5
12 12
, )
Correct Answer: B) ( 125 , 125 )
12
Rationale: Substitute y=x : 3 x+ 2 x=12 , so 5 x=12and x= y = .
5
Q7. Solve the system x +2 y =8and 3 x−2 y=8 .
A) ( 3,2 )
B) ( 2,3 )
C) ( 4,2 )
D) ( 4,4 )
Correct Answer: C) ( 4,2 )
Rationale: Adding the equations gives 4 x=16, so x=4. Substitution into
x +2 y =8gives y=2.
Q8. A theater sells adult tickets for $12 and child tickets for $8. If 20
tickets generate $200, how many of each type were sold?
, A) 15 adult and 5 child
B) 5 adult and 15 child
C) 12 adult and 8 child
D) 10 adult and 10 child
Correct Answer: D) 10 adult and 10 child
Rationale: Let a+ c=20and 12 a+8 c=200. Substitution gives a=10 and c=10 .
Q9. Which description represents the graph of y >2 x−1?
A) A dashed line y=2 x−1with the region above the line shaded
B) A solid line y=2 x−1with the region below shaded
C) A dashed line y=−2 x +1with the region above shaded
D) A solid line y=−2 x +1with the region below shaded
Correct Answer: A) A dashed line y=2 x−1with the region above the line
shaded
Rationale: A strict inequality uses a dashed boundary, and y >¿indicates
points above the boundary line.
Q10. Which point satisfies both x + y ≤ 6 and x ≥ 2?
A) ( 1,2 )
B) ( 3,2 )
C) ( 5,3 )
D) (−, 24 )
Correct Answer: B) ( 3,2 )
Rationale: For ( 3,2 ) , 3+2=5≤ 6 and 3 ≥ 2.
Q11. A store sells 30 pens consisting of $3 pens and $5 pens. Total
sales are $120. How many $5 pens were sold?
A) 10
B) 12
C) 15
D) 20
Correct Answer: C) 15
Rationale: Let x + y=30and 3 x+ 5 y =120. Subtracting 3 x+ 3 y =90gives 2 y=30 , so
y=15 .
