1. MTH-4101-2 B
Equations & Inequalities II
1. Without calculating, what is the solution of the system of equations below?
y
x
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2. Without calculating, determine the solution of the system of equations below:
1) x + −=
y 3 0
2) 2 x −−
y 9 =0
x y x y
0 3 0 -9
1 2 1 -7
2 1 2 -5
3 0 3 -3
4 -1 4 -1
5 -2 5 1
6 -3 6 3
ANS: ___________________________________
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3. Without calculating, express as a system of equations of the first degree in two
variables.
Nick is twice Richard’s age. If the difference between their ages is 30, what is the
age of each man?
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2. 4. Solve graphically the system of equations. Set up tables of values, identify the
type of lines and determine the solution set.
y
1) 2 x −−
y 8 =0
2) −−
x 1 =2y
x
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5. Solve graphically the system of equations. Set up tables of values, identify the
type of lines and determine the solution set.
y
1) − +=
2y x 0
2) 3x − =
4y −
8
x
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3. 6. Solve each system of equations by a method of your choice:
a) 1) 2x −3y =7
2) − + =( y +
x 2 9 1)
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b) 1) y +2x =31
2) 2 y −=
x 12
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c) 1) 2y + =
x 0
3 5
2) 4
x+ =y
2
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4. 7. Jack and Isabelle had a combined amount of $210. Jack spent one-third of what
he had, and Isabelle one-fifth. The sum of the expenses totaled $64. How much
did each of them start out with?
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8. Cut 25 into two parts, such that the sum of six times one part and eight times the
other part is 170. What are the values of the two parts?
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9. Find two numbers whose difference is 20 and one third of their sum is 40.
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5. Given the system of inequalities represented below:
y
1) x + ≤
y 2
2) − +≥
2x y −
4
x
State whether or not the given ordered pairs are solution-pairs of the system.
Answer by yes or no.
a) (0, 0) ______________
b) (4, 1) ______________
c) (–1, 1) ______________
d) (0, –2) ______________
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10. Draw the graph representing the solution set of the following system of
inequalities:
y
1) y + x ≤ 3
2) y – 2x ≥ –3
x
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6. 11. Draw the graph representing the solution set of the following system of
inequalities:
y
1) y – 2x ≥ 4
2) y <2
x
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