MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1

This document is the assignment for Module 3 Lesson 3 of the MAT 1100 Quantitative Reasoning course. It includes solving a system of equations, determining if given ordered pairs are solutions, and analyzing a double line graph.

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1
Student Name:
Match the system with the correct graph.
1) x + y=−5
x− y =−1
A) B)
C) D)
Solution: Let’s first find the point of intersection of the system of equations
Use elimination method:

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1
Add equation (1) and (2) we get
Substitute the value of x in any of equations we get . Hence, the point of intersection is which
lies in 4rth quadrant. Therefore the best graph is option (C).
2) Decide whether the ordered pair (-1, -4) is a solution of the given system.
x− y =5
x + y=−3
A) No B) Yes
Solution: Substitute in given system and check whether they satisfied or not.
And
Since, ordered pair does not satisfied the given system, hence not a solution. Therefore option (A) is
correct.
3) (-5, 5)
2 x+ y =−5
3 x+ 2 y =−5
A) No B) Yes
Solution: The answer is yes.
Solve by the elimination method.

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1
4)
Solution: Add both equation we get,
Substitute x = 1 in first equation we get,
Hence, the required solution is
5)
Solution: Subtract second equation from first equation we get,
Hence, the system of equations has no solutions.
6) - = -18
+ = -9
A) {(-12, 0)} B) {(12, 0)} C) {(0, -12)} D) {(0, 12)}
Solution: Multiply 2nd equation by 2 and the subtract from first equation we get,

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1
Substitute y = 0 in first equation we get, x = -12. Hence, the required solution set is
Therefore, option (A) is correct.
Solve by the substitution method.
7)
Solution: Substitute from fist equation in 2nd equation we get
Substitute in equation we get
Hence, the required solution is
8)
Solution: Substitute from first equation in 2nd equation we get,
Since, last expression is true for every values of x and y. therefore, the system has infinitely many solutions.
That is the solution set is
9) x + y = 0
x – y = 14
A) {(-7, -6)} B) ∅ C) {(6, -6)} D) {(7, -7)}

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 1
Solution: from first equation . Substitute this value in 2nd equation we get
. Now substitute x = 7 in 2nd equation we get y = -7. Hence, the solution set is .
Therefore, option (D) is correct.
10) The double line graph below shows the number of Acme Superstores vs. the number of General
Superstores.
a) In what years was the number of General stores greater than the number of Acme stores?
Solution: From the graph, it is observed that number of General stores greater than the number of Acme stores
in the years 2000 and 2002.
b) In what year was the number of Acme stores approximately equal to the number of General stores?
Solution: From the graph, it is observed that number of Acme stores approximately equal to the number of
General stores in year 1999.