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Solving systems of equations

3.) Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

5u+v=9
5u=v+21
What is the solution of the system of equations? ____________________
(Type an ordered pair . Type N if there is no solution. Type R if the solution is all real number.)
Is the system consistent or inconsistent?
A.)___________inconsistent
B.)____________consistent

Are the equation dependent or independent

A) Dependent_______________
B) independent_______

8.) Solve by the substitution method.
2x-5y=0
4x+36=y
What is the solution of the system?
(-10,-4)
(Type an ordered pair. Type N if there is no solution)

9) Solve by the substitution method.
4m+n=18
m-4n=30
What is the solution of the system.
(6,-6)
(Type an ordered pair. Type N if there is no solution)

10.) Solve by the substitution method>
6x+5y=-16
-8x+y=52
What is the solution of the system.
(-6,4)
(Type an ordered pair. Type N if there is no solution)

11.) Solve by the substitution method.
5x+3y=2
-6x+y=16

What is the solution of the system?
(-2,4)
(Type an ordered pair. Type N if there is no solution)

12.) The perimeter of a rectangle is 84m. The length is 9m more than twice the width. Find the dimensions.
What is the length?
____________m (Simplify your answer)

What is the width?
____________m (Simplify your answer)

13.) Hockey teams receive 2 points when they win and 1 point when they lie. One season a team won a championship with 63 points. They won 12 more games than they tied. How many wins and how many ties did the team have?

How many wins did the team have? ________________
How many ties did the team have? ___________________

14) Solve by the elimination method.
x+8y=25
-x7y=20

What is the solution of the system?
(1,3)
(Type an ordered pair. Type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many solutions.)

15) Solve the system by the elimination method.
5x+5y=-11
7x-3y=17
What is the solution to the system?_______________

(Type an ordered pair . Type an integer or friction. Type N if there is no solution. Type 1 if there are infinitely many solutions.)

16.) Solve by the elimination method.
0.3x-0.2y=4
0.2x+0.3y=

What is the solution of the system?_______________ (Type an ordered pair . Type an integer or friction. Type N if there is no solution. Type 1 if there are infinitely many solutions.)

17) Solve by the elimination method.

6x-9y=13.5
7y-2x=-6.5

What is the solution of the system?_______________ (Type an ordered pair . Type an integer or friction. Type N if there is no solution. Type 1 if there are infinitely many solutions.)

18) Solve by the elimination method.

0.05x+0.25y=11
0.15x+0.05y=12

What is the solution of the system?_______________ (Type an ordered pair . Type an integer or friction. Type N if there is no solution. Type 1 if there are infinitely many solutions.)

19.) The perimeter of a rectangle is 134 inches. The length exceeds the width by 61 inches. Find the length and the width.
The length is _________inches.
(Type an integer or a decimal)

The width is __________inches.
(Type an integer or a decimal)

20. The Everton College store paid $1746 for an order of 47 calculators. The store paid $10 for each scientific calculator. The others, all graphing calculators, cost the store $54 each. How many of each type of calculator was ordered?

The store ordered_______scientific and _________graphing calculators.

21.) Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out three times as many units of plywood as lumber. It makes a profit of $25 on a unit of lumber and $40 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $15080.
Snooker Lumber must produce and sell _____units of lumber and _______units of plywood to make a profit of $15080.

22.) A disc jockey must play 14 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 11 min, how many 30-second commercials were played that hour? How many 60-second commercials?

How many 30-second commercials were played per hour?_______________

How many 60-second commercials were played that hour?__________

23.) Soybean meal is 18% protein; cormeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 16% protein?

How many pounds of the cornmeal should be in the mixture?
_______________pounds

How many pounds of the soybean meal should be in the mixture?
________________pounds

24. A student makes a $9.25 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?

How many quarters are there in the change? ________________

How many fifty-cent pieces are there in the change? ____________

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Solution Summary

A step by step solution detailed solution is provided to explain the concept of consistent/inconsistent, dependent/independent, solving system of equations by elimination/substitution and graphing system of equations.

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