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Math 11
Chapter 5 Study Guide
1. Solve using the graphing calculator
y = 2x – 4
x + 3y = – 5
The solution is (
,
)
2. Which of the following systems has (8, -3) as a solution?
a) 3x + 4y = =23
b) 3x + 4y = -23
c) 4x + 3y = 23
2x + 5y = -31
2x – 5y = 31
2x – 5y = -31
3. Solve by addition or subtraction: (2 marks each)
a) 4x + 3y = 10
5x + 4y = 13
4. Solve by substitution: (2 marks each)
a) 3x – 4y = 2
-x + y = 4
d) 4x – 3y =23
2x – 5y = 31
b) 6x + 2y = 0
7x + 3y = 2
b) y = 2x 2 - 1
y=x-1
5. Determine whether each linear system has one solution, no solution or infinitely many solutions. Explain
your reasoning (2 marks each)
a) 2x + 5y = 8
x+y=2
b) 3x + 5y = 2
3x – 5y = 2
# of solutions: _____
reason: ___________________________
# of solutions: _____
reason: ___________________________
6.
When Valerie rented a car for 5 days and drove 600km, the charge was $370. When her friend Vincent
rented the same car for 4 days and drove 500 km, the charge was $300. Determine the charge per day and
the charge per kilometer. (4 marks)
per day _________
per kilometer _______
11. Marnia had $40 000 to invest. She invested part of her money in bonds paying 4% per annum and
the remainder in a GIC paying 6% per annum. The total interest earned after one year was $1950. Let
x represent the money invested in the bond. Let y represent the money invested in the GIC. Which
system of equations best represents this situation?
a. x  y  1950 and 4 x  6 y  40 000
b. x  y  1950 and 0.04 x  0.06 y  40 000
c. x  y  40 000 and 4 x  6 y  1950
d. x  y  40 000 and 0.04 x  0.06 y  1950
7. Solve:
(3 marks)
5a + b – c = 9
3a + b + 2c = 17
a + 2b + 3c = 20
8. A 10 m length of string is cut into three pieces x,
y, and z. If the first piece is doubled, the total length
is 13m. The sum of twice the first, the second, and
three times the third is 22. What are the lengths of
the string.(4 marks)
a = __________
b = __________
x = __________
c = __________
y = __________
z = __________
9. Graph the inequality 10x – 5y < 15. Be sure
to shade the appropriate region of your graph.
(3 marks)
10. Given the equation 3 x  4 y  8 , create
another equation to make a linear system
with: (1 mark each)
y

Do not use 3x + 4y = 8 as one of the answers

a) one solution a) __________

b) no solution b) __________

x
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










12. Graph the following
x –y < 3
x + 2y < 4
(3 marks)
y




x












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c) infinitely many solutions c) __________