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# Algebra: Elimination and Substitution Methods

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1. Solve the following system of equations using the Substitution method:
5X-7Y= - 18
4X+3Y= 20

2. Solve the following system of equations using the elimination method:
2X-3Y=12
-2X+3Y=12
Solution: Computation of the Equations
2X-3Y =12
-2X+3Y =12

3. A total of \$80,000 is invested in two funds paying 2.3% and 3.1 % simple interest. The total annual interest is \$2000. How much is invested in each fund?

4. Find the point of equilibrium for a system that has a demand equation of p=49-0.0003X and a supply equation of p=33+0.00002X

https://brainmass.com/math/algebra/algebra-elimination-and-substitution-methods-576189

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## 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?

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