Download Solving 2 x 2 Systems of Equations

Math 11
Solving 2-Variable Systems (Practice)
1. The graph describes two phone plans.
A
16
(a) Write the equation for each plan.
14
Plan A_________________
B
12
Cost ($) 10
Plan B_________________
8
(b) Describe Plan B in words.
6
(c) Describe when Plan A would be the best choice.
4
2
(d) When do the plans cost the same amount?
10
20
30
40
50
60
Time (min)
2. The charges for a one day car rental for two dealers are described by the equations, where c
represents cost in dollars and n represents the number of kilometers driven.
Dealer A:
c = 0.33n + 15
Dealer B:
c = 0.25n + 21
(a) Describe each plan.
(b) When do both plans cost the same amount?
(c) Which plan would you chose if you intended to drive about 90 km?
3. Solve the following using the substitution method:
(a) 17 x + 5y = 193
x – 19y = 513
(b) y = 2x – 21
y = 3x – 37
4. Solve the following systems by graphing:
(a)
y  2x  1
y  4x  1
(b)
4 x  2 y  6
y  2 x  1
(c)
2x  3 y  0
6 x  2 y  14
5. Solve the following using the elimination method:
(a) 1.3x + 2.5y = 0.1
4.2x – 6.3y = 14.7
(b) 2x + 9y = -219
3x – 19y = 289
6. Solve using the most convenient method:
(a) 14x – 13y = 390
y = 2x – 42
(d)
(g)
0.3x  0.2 y  0.2
0.1x  0.4 y  0.3
3 y  15 x  12
y  5x  3
(b) x + y = 7
x – y = -3
(c) 2x + 3y = 11
3x = 3
1
1
x y 3
2
2
(e)
1
1
x y 3
4
2
(f)
(h)
x  3y  4 2
3x  y  2 6
2y  x  3
8 y  4 x  12
Solve the following by identifying the variables, writing two equations and solving using either elimination
or substitution.
7. A farmer with an unusual specialty raises only turkeys and racehorses. In reply to a questionnaire
from the department of agriculture, he indicated that the number of animals on his farm consisted of
1271 heads and 2624 feet. How many horses and how many turkeys does he have?
8. Ariana bought 50 stamps at the post office. Some were 35¢ and the rest were 17¢ stamps. If the
total value of the stamps was $10.30, how many 17¢ stamps did she buy?
9. A regular widget is held together with seven bolts and a super widget requires ten bolts. In one day’s
production, the widget factory used 2590 bolts to produce 325 widgets. How many of these were super
widgets? How many were regular widgets?
FYI: In general, widget (pronounced WIJ-it) is a term used to refer to any discrete object, usually of some
mechanical nature and relatively small size, when it doesn’t have a name or when you can’t remember it.
10. A rectangle has a perimeter of 32 cm. If 3 cm is taken from the length and added to the width, the
rectangle becomes a square. Find the dimensions of the original rectangle.
11. The sum of two integers is 36, and their difference is 4. Find the integers.
12. Find two numbers whose sum is 196 if the larger exceeds the smaller by 8.
13. A paper boy collected $6.55, part in nickels and part in dimes. If the number of nickels was 6 more
than one-half the number of dimes, how many nickels were there?
14. On your 16th birthday you receive $1000 to invest for college. You “diversify” by splitting it in two
parts and investing in two different stocks, hoping for the best. By your 17th birthday you have earned
$110 on it, and the reports indicate that one stock paid 8%, while the other paid 12%. How much was
originally placed in each account?
Solving 2-Variable Systems – ANSWERS
1. (a) A: y = 0.24x
B: y = 0.4x + 8
(b) cost is $8 base fee plus $0.40 per min
(c) A is best for more than 50 min
2. (a) A: $15 plus $0.33 per km
(d) 50 min.
B: $21 plus $0.25 per km
(b) 75 km
(c) A
3. (a) x = 19, y = -26
(b) x = 16, y = 11
4. (a) x = 1, y = 3
(b) x = -1, y = 1
5. (a) x = 2, y = -1
(b) x = -24, y = -19
6. (a) x = 13, y = -16
(b) x = 2, y = 5
(d) x = 1, y = -0.5
(e) x = 8, y = -2
(g) no solution
(h) infinite number of solutions
7. 41 horses, 1230 turkeys
8. 40 17¢ stamps
9. 220 regular, 105 super
10. 5 x 11
11. 20 & 16
12. 102 & 94
13. 31 nickels
14. $250 in 8% stock, $750 in 12%
(c) x = 3, y = 2
(c) x = 1, y = 3
(f) x 
2,
y 6