MPM2D
1.1 Worksheet
1. Solve the following linear systems by graphing. Check the solution algebraically.
𝑦 =𝑥−5
and
1
𝑦 =− 𝑥+7
2
2. Solve the linear system 𝑥 + 4𝑦 + 24 = 0 and 2𝑥 − 3𝑦 + 15 = 0 by graphing.
3. Solve the linear system 𝑦 = 0.75(𝑥 − 5) and 𝑦 = 0.4(𝑥 − 12) by graphing.
4. Taxi fares in Yellowknife, NT, include a $4.50 base fee plus $2.00 per
kilometre. A proposal may be considered to reduce the base fee to
$3.00 and increase the rate to $2.25 per kilometre.
a) Write the equations for a linear system to represent this situation.
b) Plot the linear system on the grid provided.
c) State the solution to the linear system and explain its meaning in
this situation.
Answers:
1. The solution is the point of intersection (𝑥, 𝑦) = (8, 3) shown in the following graph:
2. The solution is the point of intersection (𝑥, 𝑦) = (−12, −3) shown in the following graph:
3. The solution is the point of intersection (𝑥, 𝑦) = (−3, −6) shown in the following graph:
4. a) The equation for the current taxi fare is 𝑐 = 4.5 + 2𝑑 and the
equation for the proposed taxi fare is 𝑐 = 3 + 2.25𝑑.
4. b) This linear system is plotted on the following graph.
4. c) The solution to this linear system is the point of intersection at
(6, 16.5) on the graph. The meaning of this point is that both the
current and proposed taxi fares will be the same when the trip
distance is 6 km which will cost $16.50 (shorter trips are more
expensive under the current system but longer trips would be
more expensive under the proposed system).