Download Properties of Systems of Linear Equations

LESSON 5: PROPERTIES OF SYSTEMS OF LINEAR EQUATIONS
Learning Outcome: Learn to determine the numbers of solutions of
different types of linear systems.
Work in a group of 3. You will need a graphing calculator.
Each linear system below contains the equation -2x + y = 2
Solve each linear system by graphing:
System1
System 2
System 3
-2x + y = 2
-2x + y = 2
-2x + y = 2
2x + y = 2
-2x + y = 4
-4x + 2y = 4
Share your results with your group.
How many solutions does each linear system have?
When two lines are graphed on the same grid, they do not always have
exactly one point of intersection. Parallel lines do not intersect at all. So, a
system of parallel lines has no solution.
Coincident lines have an infinite number of solutions because the lines are
equivalent. They overlap.
When you attempt to solve a linear system of two equations in two
variables, there are only three possibilities. You can determine the number
of solutions using different methods.
Possible Solutions for a Linear System
Intersecting Lines
One solution
Parallel Lines
No Solution
Coincident Lines
Infinite solutions
Ex. Predict the number of solutions for each system of linear equations.
Explain your reasoning, and then confirm each answer by graphing the
linear system.
a) 𝑦 = 2𝑥 − 3
1
𝑦 = 𝑥+3
2
b) 4x + 10y = 30
2x + 5y = 35
c) 10x – 6y = -12
21y = 42 + 35x
Ex. Given the equation -6x + y = 3, write another linear equation that will
form a linear system with:
a) exactly one solution:
b) no solution:
c) infinite solutions
Ex. A particular dog-mushing race is 13km long. The distance and speed
for several competitors at a certain time during the race are shown in the
table of values.
Competitor A
Competitor B
Competitor C
Competitor D
Current distance travelled (km)
6.0
5.0
4.0
4.0
Current Speed (km/h)
24
32
24
24
Assume the racers continue at their current speeds. For each pair of
competitors below,
 Write a system of linear equations representing their travel from
this point forward
 Graph each system of linear equations
 Identify and interpret the solution to each linear system
a) competitors A and B
b) competitors A and C
c) competitors C and D
Assignment: pg. 448-449 #4-12, 14-22