The document contains practice problems for the BC Math 10 Provincial Exam, addressing various topics such as systems of equations, linear equations, and word problems related to real-life scenarios. Solutions for each problem are provided, along with calculations and values needed to arrive at the answers. Key areas include solving equations, determining intersections, and applying mathematical concepts in practical contexts.

1. www.provincialexam.ca | BC Math 10 Provincial Exam Practice Examples
Systems Practice Test Name: ______________________ Period: _____
1) How many solutions does this system of equations have?
2 3
2 1
y x
y x
Answer: 0
2) How many solutions does this system of equations have?
5
2 2 10
x y
y x
Answer:
3) Solve, in other words find the point of intersection of the following linear system:
3 1
2 5 3 0
y x
y x
Answer as a decimal number (two decimal places).
Answer: ( 0.09,1.27)
4) In which quadrant does the following system contain a solution?
3 1
1
1 5
2
y x
x y
Answer: Quadrant I
5) Solve for y in the following system of equations (as a decimal number):
2 1
2 4 15
x y
x y
Answer: 2.125

2. 6) Which of the following systems has a solution of ( 2,5)?
A.
7
2 3 8
x y
y x
B.
2 1
3 2 16 0
x y
x y
C.
3 5
2 3 0
x y
x y
D.
4 0
2 5 8
x y
x y
Answer: B
7) Determine the x -value of the point of intersection for the system
represented by
2
( ) 1
3
h x x and ( ) 2z x . Answer as a decimal.
Answer: 1.5
8) Solve for y . Answer with two decimals.
2 3 8
3
x y
x y
Answer: 2.67
9) There are two types of coins. 8 small coins and 12 large coins weigh 200 grams.
4 small coins and 20 large coins weigh 300 grams. How much does a single
LARGE coin weigh? Answer to the nearest tenth of a gram.
Answer: 14.3 g

3. 10) What value of w gives a linear system with infinite solutions?
( 2) 5x w y
3 5x y
Answer: 1
11) The graphed lines of 5x By and 2 7x By intersect at (2, 3).
What is the value of B ?
Answer: 1
12) A wedding hall rental costs $1210 for the hall plus $20 per person for food.
If each guest gives $60 cash, how many guests must attend to make a PROFIT?
Answer: 31
13) You invest a total of $2000 between two stocks. One stock earns 12% interest
and other stock earns 4% interest. You earn $160 interest on your two stocks at
the end of the year. How much did you invest in the stock that earned 12% interest?
Answer: $1000
14) A bartender mixes two alcoholic beverages. Drink A is 5% alcohol by volume.
Drink B is 40% alcohol by volume. We want to find how much of drink A is
needed to mix with drink B to make a 500 mL mixture that is 30% alcohol by volume.
Just set up the two equations (this will save you time).
Do NOT bother solving for A and B.
Answer:
500
0.05A 0.40B 500 0.30
A B

4. 15) Two jets have a cruising speed of 450 km/h without wind. The first plane flies
for 6 hours with a tailwind. The second plane flies for 8 hours in the opposite
direction against a headwind. The second plane flies 100 km more than the first plane.
Determine two equations that could be used to solve for the wind speed, w , and
the distance travelled by the first plane, d . Just the equations are fine (save time).
Do NOT solve w and d .
Answer:
(450 )(6)
100 (450 )(8)
d w
d w
16) A canoe took 4 hours to travel 18 km with the current. On the return trip, the
canoe took 6 hours to travel the same distance against the current. When the canoe
travels with the current it travels faster than normal. How fast does the canoe travel
WITH the current? One decimal accuracy.
Answer: 4.5 km/h
17) In your sales job you are paid a fixed amount each month plus a percentage of the
sales you make. You are paid $3,000 a month when you sell $20,000 worth of
merchandise. You are paid $4,000 a month when you sell $30,000 worth of
merchandise. What is your fixed income?
Answer: $1000