1) The document discusses solving systems of equations and inequalities. It contains 13 problems involving setting up, graphing and solving systems of linear and nonlinear equations and inequalities. 2) The problems cover a range of techniques for solving systems, including substitution, elimination, graphing, and applying constraints to identify variable values that satisfy simultaneous relationships. 3) The document provides practice with setting up and solving different types of systems, as well as interpreting solutions in the context of word problems about rates, prices, ages and coin values.

1. MTH-4101-2 D
Equations & Inequalities II
1. Without solving, express the following as a system of two equations, making
sure to define your variables.
The difference between two integers is 3. Twice the smaller is equal to five
less than half the larger.
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2. Determine the solution set for the following system of equations:
1 2
x y x y
-2 0 -1 1
1 -1 0 0
4 -2 1 -1
7 -3 2 -2
10 -4 3 -3
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3. What is the solution of the following system of equations? Write your answer
as an ordered pair.
y
x
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2. 4. Using the method of your choice, determine the solution of the following
system of equations; write your answer as an ordered pair:
1) y = 8x – 12
2) 4y = 22 – 3x
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5. Solve the following system of equations graphically. Write your solution as an
ordered pair.
y
1) 4y = 3x + 4
2) y = -4x + 12
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) y = 7/5x – 9
2) 4y = 3x + 3
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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) y = 3/2x +18
2) 4/3y = -2x
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8. Given the adjacent system of inequalities, state whether or not the following
points belong to the solution set: y
(-1, 3)
(2, -4)
(5, 7) x
(6, 2)
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4. 9. Solve the following system of inequalities graphically:
y
1) y ≤ -1/5x + 2
2) 3x > 2x – 1
x
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10. Solve the following system of inequalities graphically:
y
1) y < 3/2x – 2
2) y ≥ -1/4x + 3
x
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5. 11. A woman has 64 coins in her purse consisting of pennies and nickels. If the
total value of the coins is $1.72. How many of each type of coin does she
have?
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12. Matthew is 4 years younger than Debbie. In two years he will be two years
older than half Debbie’s present age. How old are Matthew and Debbie now?
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13. Two adult day passes and one student pass at Mont Tremblant costs $131.89;
while 3 adult passes and 4 student passes costs $ 277.81. What are the prices
for each pass?
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