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Use the addition or subtraction method to solve each system of equations.
A
1. x-y=o
x+y==4
+ 2y == 0
-x + 2y =8
7. 5x + 3y == 5
4x + 3y == 10
10. 3x + 4y == 4
6x + 7y == 13
13. 2x + 3y == -1
4. 3x
5x - 6y == 38
16. -3x+2y==7
9x-5y==-10
B 19. 2x + 5y == -1
3x + 4y == 9
+ 4y == 12
+ 3y == 10
25. 6x + 8y == 4
22. 3x
2x
~x
+ 2y == 1
2
28. 17x - 3y = 9
-SIx + 9y == -27
2. 2x + 3y == 5
4x -3y == 1
3. 3x + 2y
5. 4x - 3y == 18
-4x + 5y == -22
6. 2x - 5y == 3
-x+5y==6
8.5x+2y==-7
5x + 4y == 1
9. 5x + 2y == 3
15x+7y==-2
=
3
3x-y==3
11. 3x + 7y = -12
5x + 14y == -13
12. 5x - 6y == 92
15x + y == 48
14.5x+12y==8
2x-3y==-28
15. 8x + 3y == 14
-2x + 5y=8
17. 4x + 3y == 15
2x -9y ==-3
18. 5x + l2y == -21
-lOX + 3y == -39
20. 2x - 3y == -13
-3x + 4y = 14
21. 2x - 5y = 20
3x + 2y == -27
23. 2x - 3y == 2
6x -9y == 10
24. -5x + 2y = 10
2x + 3y == -23
26. -3x+ 2y== 2
6x -4y == 1
27. 5x -2y ==-5
7x-Sy == -51
29. -3x-5y=67
4x-3y==-12
30.4y-3x==21
3y + 2x =37
WRITIEN EXERCISES
Solve each problem using two equations in two variables.
A 1. The sum of two numbers is 40. Their difference is 14. What are the numbers?
2. The difference between two numbers is 28. The greater is 81eS$than twice the
lesser. Find the numbers.
"
3. Adam is 10 years older than Eva. The sum of their ages is 56 years. How old is
each person?
4. The sum of Emil's and Rosa's ages is 27 years. Nine years ago Emil was twice as
old as Rosa was then. How old is each person?
5. The width of a rectangle is half the length. The perimeter is 42 cm. Find the
dimensions of the rectangle.
6. The perimeter of an equilateral triangle is 6 ern more than the perimeter of a
a square, The length of a side of the square is 3 em less than the length of a
side of the equilateral triangle. Find the area of the square.
7. Two angles are supplementary. The measure of one is 16 less than 3 times the
other. Find the measure of each angle.
8. Two angles are complementary. The measure of one is 9 more than twice the
other. Find the measure of each angle.
9. Keith has $265 in $5 bills and $10 bills. He has 37 bills in all. How many of
each kind does he have?
10. Heidi has 12 more $5 bills than $2 bills. Altogether she has $137. How many
of each kind does she have?
11. Man-sun traveled by train for 3 h and by bus for 1 h to visit his cousin who
lived 334 km away. The average rate of the train was 16 km/h faster than the
bus. How fast did the train travel?
12. The Twesmey twins left their house at the same time, driving in opposite
directions. Nora drove 5 km/h slower than Dora. After 4 h they were 456 km
apart. How far did Dora drive?
13. Tickets to the "Potatoes" concert cost $5 and $8. If 960 tickets were sold for
a total of $5652, how many tickets were sold at each price?
14. Admission to the Stratham Fair is $4 for adults and $1.50 for children under
12. On Friday 4019 people went to the fair. The gate receipts for that day
were $11,568.50. How many adults and how many children attended the fair
on Friday?
8 15. How many liters of a 10% alcohol solution and how many liters of a 20%
alcohol solution must be mixed together to make 10 L of a 12%alcohol solu­
tion?
16. How many kilograms of a 5% salt solution and how many kilograms of a 15%
salt solution must be mixed together to make 45 kg of an 8% salt solution?
17. Peanuts worth $4/kg were mixed with almonds worth $7/kg to produce 11.5 kg
of nuts worth $55. How many kilograms of each type of nut were used?
18. A grocer carries two brands of coffee, one worth $5.50/kg and the other worth
$6.50/kg. How many kilograms of each brand should be mixed together to
produce 44 kg of coffee worth $5.75/kg?
19. A parking meter contains 47 coins in dimes and quarters for a total of $5.45.
How many of each coin does the meter contain?
20. A beverage machine contains 59 nickels and dimes for a.total of $4.55. How
many of each coin does the machine contain?
21. A motorboat travels 160 km upstream in 8 h. It travels the same distance
downstream in 5 h. What is the rate of the boat in still water?
22. Mimi is one third as old as George. In 5 years she will be one half as old as
George. How old is Mimi?
23. Dr. Kaye has invested a total of $8000, part in a 90-day notice account paying
9% interest per year and the rest in a regular savings account paying 6% per
year. How much was invested in each account if the total interest earned in one
year was $675?
24. Last year Joe- Raintree invested $300 more in a stock paying a 6% dividend
than he did in a stock paying a 5% dividend. That year he earned $43 more in
dividends from the stock paying the higher dividend. How much did he invest
in each stock?
C 25. Sarah began her round trip canoe trip from Keene Valley to Keeseville at
8 AM. She traveled a total of 108 km and returned to Keene Valley at 5 PM.
If she spent all but 1 h of that time traveling on the river, and if the return trip
took three times as long as the outbound trip, how fast was the current?
26. The perimeter of a rectangle is 56 cm. If the length were halved and the width
doubled, the perimeter would be 58 em. How long is the original rectangle?
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