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Question 86569: 6.1
I. Solve each system by graphing, and classify the system as dependent or independent,
consistent or inconsistent.
1. {2x+3y=-7
{3x-4y=2
2. {3x-2y=10
{4x+y=6
3. {x-9=3y
{x+2y=-1
4. {2x+3y=2
{3x-4y=-14
5. {2x+4y=6
{5x-3y=2
6. {y=3x
{x+21=-2y
7. {x+y=6
{3x-4y=4
8. {12x-9y=27
{8x-6y=18
9. {a+b=8
{1.5a+2b=13.5
10. {5x-y=3
{y=5x-3
11. {2x-3y=7
{2x+3y=7
12. {4/3x+1/5y=3
{2/3x-3/5y=5
II. Use a calculator to solve each system of equations to the nearest hundredth.
13. {y=3x-2 14. {y=1/4x+3 15. {y=-x+7
{y=-0.5x+5 {y=-2x+21 {8=2x-y
16. {y=0.125x-3.005 17. {12y=4x-16 18. {1/2x+1/3y=1
{y=-2.58 {9y-3x=3 {3x+2y=6
19. The perimeter of a rectangular picture is 36 inches. Twice the width exceeds the length by 2 inches. What are the dimensions of the picture?
20. Find a and b so that and are consistent and dependent equations.
6.2
Part I. Solve each system by substitution.
1. {3x+y=7
{4x+2y=16
2. {2x+3y=4
{x-2y=16
3. {2x+y=5
{3x-3y=3
4. {2x+2y=4
{x-2y=0
5. {y=x+3
{y=2x-4
6. {4x+5y=-7
{3x-6y=24
7. {2s-5t=22
{2s-3t=6
8. {4x+2y=20
{y=x-2
9. {2x=5+4y
{2y=8+x
10. {4y+30=10x
{5x-2y=15
11. {s=10+5t
{2s=40+4t
12. {12y-5z=19
{12y+16z=40
Part II. Solve each system .
13.{x-2y+z=-9 14. {2a+b=2 15. {x+y+z=-1
{2y+3z=16 {5a=15 {3x-2y-4z=16
{2y=4 {a+b+c=-1 {2x-y+z=19
16. The sum of three numbers is 20. The first number is the sum of the second and the third. The third number is three times the first. What are the three numbers?
17. Melissa works at Angela’s Pizza. Her last three orders were 5 slices of pizza, 2 salads and 2 sodas for $9.75; 3 slices of pizza, 2 salads, and 1 soda for $7.15; and 2 slices of pizza, 1 salad, and 1 soda for a total of $4.35. What are the individual prices for pizza, salad, and soda at Angela’s?
6.3
Part I. Review: Solve each system by substitution.
1. {2x+y=4 2. {x-9=3y 3 {c+3d=8
{3x+2y=1 {x+2y=-1 {1/3c+d=9
Part II. Solve each system by elimination
4. {2x+y=11 5. {6x+3y=6 6.{4x-2y=5
{3x+2y=1 {8x+5y=12 {2x=y-1
7. {4p+5p=7 8. {7b-5c=11 9.{1/3x+1/2y=7
{3p-2q=34 {-4c-2b=-14 {2/3x-y=-2
10. {5m+2n=-8 11. {2y-4x=18 12.{3x-5y=17
{4m+3n=2 {-5x+3y=23 {4x+5y=46
Part III. Solve each system
13. {3x-6y+3z=33 14. {6a-2b=18 15.{1/x-1/y=5/8
{2x-4y+2z=22 {3b+5c=-34 {3/x+2/y=5/8
{4x+2y-z=-6 {a+bc=-28
hint: eliminate x in the first two equations.
hint: let m=1/x
and n=1/y
6.4
Part I. Use two variables and two equations to set up each problem. Do not solve.
1. One integer is twice another and their sum is 96. Find the integers.
2. The sum of two integers is 38 and their difference is 12. Find the integers.
3. Three times one integer plus another integer is 29. If the first integer plus twice the
second is 18, find the integers.
4. Twice one integer plus another integer is 21. If the first integer plus 3 times the
second is 33, find the integers.
Part II. Use two variables and two equations for each problem. Solve the systems by any method you choose, and write the answer in the appropriate form.
5. A rancher raises five times as many cows as horses. If he has 168 animals, how
many cows does he have?
6. A landscaper used 100 pounds of grass seed containing twice as much bluegrass
as rye. He added 15 more pounds of bluegrass to the mixture before seeding a
lawn. How many pounds of bluegrass did he use?
7. A youth group with 26 members is going skiing. Each of the five chaperones will
drive a van or a sedan. The vans can seat seven people, and the sedans can seat five
people. How many of each type of vehicle could transport all 31 people to the ski
area in one trip?
8. In a mayoral election, the incumbent received 25% more votes than the opponent.
Altogether, 5175 votes were cast for the two candidates. How many votes did the
incumbent mayor receive?
9. The drama club at Lincoln High School sells hot chocolate, and coffee at the
school’s football games to make money for a special trip. At one game, they sold
$200 worth of hot drinks. They need to report how many of each type of drink
they sold for their club records. Macha knows that they used 295 cups that night.
If hot chocolate sells for $0.75 and coffee sells for $0.50, how many of each type
of hot drinks did they sell?
Answer by Flake(45)   (Show Source):
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