1. MTH-4101-2 C
Equations & Inequalities II
1. What is the solution of the following system of equations? Write your answer as
an ordered pair.
y
x
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2. Determine the solution set for the following system of equations:
y – 4 = 3x – 1
x –3 –2 –1 0
y –6 –3 0 3
y–x=1
x –2 –1 0 1
y –1 0 1 2
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3. Without solving, express the following as a system of two equations, making sure
to define your variables.
If I buy 2 shirts and 3 ties, my bill comes to $213. However, if I buy 5 ties and 3
shirts my bill comes to $337. What is the price of a single shirt and tie?
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2. 4. Solve the following system of equations graphically. Write your solution as an
ordered pair.
1) 4y = 2 – 5x
2) 6 – 2y = 0
y
x
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5. Solve the following system of equations graphically. Write your solution as an
ordered pair.
1) 2y + x = 0
2) 3/2x = 3 – y
y
x
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3. 6. Using the method of your choice, determine the solution of the following system
of equations; write your answer as an ordered pair:
1) 1/2x – 1/3y = 1
2) 2/3x + 1/2y = –2
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7. Using the method of your choice, determine the solution of the following system
of equations; write your answer as an ordered pair:
1) x = 5y – 15
2) y = 1/5x – 1
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8. Using the method of your choice, determine the solution of the following system
of equations; write your answer as an ordered pair:
1) 5x + 2y = 4x + 8
2) 4y = 20 – 3x
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4. 9. During a Montreal Alouettes football game, I buy 2 hamburgers and 3 hotdogs
and it costs me $8.25. The next game, I buy 4 hamburgers and 5 hotdogs for
$15.25. What is the price of 1 hotdog and 1 hamburger?
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10. The difference between two numbers is 9. One-sixth the smaller number added to
one-third the larger number is equal to 12. What are the two numbers?
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11. A brother is 5 years older than his sister. Three years from now, the sister will be
three-quarters of her brother’s age then. How old are the brother and sister now?
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12. Given the adjacent system of inequalities, state whether or not the following
points belong to the solution set:
y
a) (1, 2)
b) (2½, 3/4)
x
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5. 13. Solve the following system of inequalities graphically:
1) x + 2y ≤ 4
2) 3x – y ≥ 3
y
x
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14. Solve the following system of inequalities graphically:
1) x + y < 2
2) x ≥ y + 1
y
x
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