# 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? ____________

#### 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.