Lesson 2 –Linear Systems
LINEAR SYSTEMS
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Two or more lines considered together
The solution to a linear system is the point(s) of intersection (POI)
There are 3 possible outcomes when solving a linear system.
ONE SOLUTION
INFINITE SOLUTIONS
Solution is a point
Solution is a line
Equivalent Systems
NO SOLUTIONS
No solution
Example ① Graph the linear system below.
−𝑥 + 2𝑦 = 6
1
𝑦 = 𝑥+3
2
What is the solution to the linear system?
Is there a way you can tell if you will have one, none, or infinite solutions without graphing?
Example ②
a)
Without graphing, determine whether each system has one solution, no solution or
infinitely many solutions.
𝑥 + 3𝑦 = −1
2𝑥 + 6𝑦 + 2 = 0
Example ③
c) 3𝑥 + 2𝑦 – 10 = 0
2𝑥 – 3𝑦 – 3 = 0
Create an equivalent linear equation for each of the following:
a) 𝑦 = 3𝑥 – 7
Example ④
b) 𝑦 = 2𝑥 – 3
2𝑥 – 𝑦 = 5
b) 𝑥 – 4𝑦 + 12 = 0
Graph each equation on the same set of axes to find the point of intersection:
𝑦 = 2𝑥 + 1
𝑦 + 𝑥 = 7