1. MTH-4101-2 A
Equations & Inequalities II
1. Without calculating, what is the solution of the system of equations below?
y
x
/5
2. Without calculating, determine the solution of the system of equations below:
x y x
1) + =5
2 3
2) 3
+ 2 y −14 = 0
x y x y
10 0 3 6.5
6 6 0 7
2 12 42 0
-2 18 6 6
0 15 12 5
/3
3. Without calculating, express as a system of equations of the first degree in two
variables.
We wish to spend $164.00 by purchasing 10 books, some costing $15.00, and
other $17.00. How many books of each price do we buy?
/5

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) − x +=
0.5 y 5
2) −+ +
x 2y 3 =0
x
/5
5. Solve graphically the system of equations. Set up tables of values, identify the
type of lines and determine the solution set.
y
1) 3x +5y =25
2) 8x −
3y =34
x
/5
6. Solve each system of equations by a method of your choice:

3. a) 1) 3x = ( y + )
2 2 9
2) 2 y =3 x
−
/10
7
b) 1) 2
x + 2 y = 31
x
2) 3
− 5 y = −23
/10
c) 1) 2 x −y =
3 5
2) 10 x − = y
25 15
/10
7. Grace said to Raymond, “7 years ago, I was triple your age then, and in 7 years,
I’ll be double your age then.”

4. Find Grace and Raymond’s present age.
/9
8. The difference between two numbers is 7. Twice the larger number plus three
times he smaller number equals 29.
Find these two numbers.
/9
9. For one day’s work, a contractor paid $632 to 5 carpenters and 2 plumbers. The
next day he paid $648 to 3 carpenters and 4 plumbers. Determine the daily salary
of a carpenter and a plumber.
/9
10. Given the system of inequalities represented below:

5. y
1) 2
+1 > 0
2) 3y – 2x < 18
State whether or not the given ordered pairs are solution-pairs of the system.
Answer by yes or no.
a) (1, 1) ______________
b) (2, –4) ______________
/4
11. Draw the graph representing the solution set of the following system of
inequalities:
y
1) 3x – 5y < 15
2) 3y – 3x ≤ –9
x
y
/8
x
12. Draw the graph representing the solution set of the following system of
inequalities:
1) 2x + 3y < 4x + 5

6. 2
2) 3x +
3
y <4
/8