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# MATH101_SLP_4-_Systems_of_Equations_and_Inequalities

Homework

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Name:
Date:
Instructor:
methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember
that your work should be clear and legible.
Write the final answer in the terms being asked such as dollars/cents, degrees, tickets,
etc.
1. Describe the three types of solutions systems of equations have when graphed.
Answer: Case 1; One Solution. The graph of this type of system of linear equations will
have two lines intersect a given point. The coordinates of the single point are the likely
solutions. Case 2: No solutions. In this the linear equations will have two parallel line.
No intersection. Case 3; Infinite number of solutions. The linear equation gives rise to
two lines that lie on top of each other. Each coordinate of one line will be also on the
second line. This means the two lines are these same equations.
2. The sum of two numbers is 30 and their difference is 2. Find the two numbers by
writing and solving a system of equations.
Calculations:
x +y = 30
x – y = 2
x=30-y
30-y-y = 2
30-2y= 2
-2y=2-30
y=14
x=16
3. Two apples and three pears cost \$3.45. Three apples and five pears cost \$5.55.
Find the cost of each type of fruit.
Calculations:
let apples be x and pears be y, therefore,

2x+3y= 3.45
3x+5y=5.55
3(2x+3y=3.45) =6x+9y=10.35
2(3x+5y=5.55) =6x+10y=11.1
-y= -0.75
y=\$0.75 per pear
x=\$0.6 per apple
4. Mary has a total of \$5000 invested in two accounts. One account pays 5% and the
other 8%. Her interest in the first year was \$331. Write and solve a system of
equations to find out how much she has invested in both accounts.
Calculations:
Let the amount invested in 5% interest a/c be x while 8% a/c be y
x+y= 5000
0.05x+0.08y=331
y=5000-x
0.05x+0.08(5000-x)=331
0.05x+400-0.08x=331
-0.03x=-69
x= \$2,300
y= \$2700
5. Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs.
less than the larger one, how much does each box weigh? Write and solve an equation
that models this scenario.
Calculations:
Let larger box weigh y lbs, therefore the smaller is (y-5) lbs
y+(y-5)=21
y+y-5=21
2y-5=21
2y=26
y= 13

y-5=8
The larger box weighs 13 lbs while the lighter one weighs 8 lbs
6. The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is
72 feet, find the dimesions of the pool by writing and solving a system of equations.
Calculations:
let the width be y and its length will be 2y+3
2((2y+3)+y)=72
2(2y+3+y)=72
4y+6+2y=72
6y=72-6
y=11
The width will be 11feet, Length will be 25 feet
7. A desk and a chair cost \$200 as a set. If the desk costs four times more than the
chair, how much does each one cost. Write and solve using a system of equations.
Calculations:
Let chair cost be x, therefore desk will be 4x
4x+x=200
5x=200
x=40
Chair costs \$40 while a desk costs \$160.
8. Rachel has 15 coins with a value of \$2.85. If the coins are either dimes or quarters,
how many of each coin does she have? Write and solve using a system of equations.
Calculations:
if the number of dimes is y, then quarters will be (15-y)
Dimes = \$ 0.10
Quarter=\$0.25
Therefore,
0.10y+ 0.25(15-y)= 2.85
0.1y+3.75-0.25y=2.85
-0.15y= -0.9
y= 6,(15-y)= 9
He had 6 dimes and 9 quarters

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MAT101 SLP4 Answer TemplateName: Date: Instructor: Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible. Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.1. Describe the three types of solutions systems of equations have when graphed.Answer: Case 1; One Solution. The graph of this type of system of linear equations will have two lines intersect a given point. The coordinates of the single point are the likely solutions. Case 2: No solutions. In this the linear equations will have two parallel line. No intersection. Case 3; Infinite number of solutions. The linear equation gives rise to two lines that lie on top of each other. Each coordinate of one line will be also on the second line. This means the two lines are these same equations. 2. The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.Calculations:x +y = 30x - y = 2x=30-y30-y-y = 230-2y= 2-2y=2-30y=14x=163. Two apples and three pears cost \$3.45. Three apples and five pears cost \$5.55. Find the cost of each type of fruit.Calculations:let apples be x and pears be y, therefore,2x+3y= 3.453x+5y=5.553(2x+3y=3.45) =6x+9y=10.352(3x+5y=5.55) =6x+10y=11.1-y= -0.75y=\$0 ...
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