# Algebra: Equations

1. How can you determine whether a system has no solution by graphing?

2. Solve by graphing:

y=x-3

y=-x+1

3. Solve by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.

3y-x=0

x-4y=-2

4. Ticket sales. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?

5. What are we trying to accomplish by adding the equations?

6. Solve by the addition method:

3x+5y=-11

x-2y=11

7. Solve by the addition method:

x/3-y/2 = -5/6

x/5-y/3 = -3/5

8. Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?

9. How are the planes positioned when a system of linear equations in three variables is independent?

10. Solve:

2x-y+3z =14

x+y-2z =-5

3x+y-z = 2

11. Solve:

2x-y = -8

y+3z = 22

x-z = -8

12. Solve:

4x-2y-2z = 5

2x-y-z = 7

-4x+2y+2z = 6

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#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

The solution to algebra equations

1. solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

x+y=10

x-y=4

2. solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

2x-y=19

2x+3y=-19

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

4u+v=33

4u=v+39

4. solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

Y=-x-9

5x-4y= -9

5. solve by the substitution method

5x-8y= -12

4x+42=y

6. solve by the substitution method

8m+n=70

m-9n=27

7. solve by the substitution method

2x+7y=5

-6x+y=51

8. solve by the substitution method

3x+4y=1

-7x+y=39

9. the perimeter of a rectangle is 42m. the length is 9m more than twice the width. Find the dimensions

10. hockey teamse receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 65 points. They won 10 more games than they tied. How many wins and how many ties did the team have

11. solve by the elimination method

x+8y=44

-x+6y=26

12. solve by the elimination method

5x+3y= -7

7x-2y=17

13. solve by the elimination method

0.3x-0.2y=4

0.4x+0.5y=1

14. solve by the elimination method

6x-9y=13.5

7y-3x= -8

15. solve by the elimination method

0.05x+0.25y=66

0.15x+0.05y=72

16. the perimeter of a rectangle is 144 inches. The length exceeds the width by 52 inches. Find the length and the width

17. the everton college store paid $1972 for an order of 52 calculators. The store paid $9 for each scientific calculator. The others, all graphing calculators, cost the store $ 56 each. How many of each type of calculator was ordered?

18. 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 $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $16320?

Snooker lumber must produce and sell ____units of lumber and ___ units of plywood to make a profit of $16320

19. 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 and 11 min, how many 30 second commercials were played that hour? How many 60 second commercials.=?

20. soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360LB mixture that is 11% protein?

21. a student makes a $9.75 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?