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Unit 1: Linear Systems
Date: ______________________
Lesson #1: Solving Linear Systems by Graphing
L.G. “I can solve a linear system by graphing.”
What is a linear system?
A linear system consists of ____________________ linear equations.
A solution to a linear system is an ordered pair (x, y) that satisfies all of the equations in the system. One technique to
solve a system is to graph both equations and determine the point of intersection (POI).
Q: In how many ways can 2 lines intersect? Graph each case below and comparing the slopes and y-intercepts.
Slopes:
Slopes:
Slopes:
y-intercepts:
y-intercepts:
y-intercepts:
Example 1: Determine the POI between the two lines y = 2x+1 and y = -x + 4. Verify the solution.
POI: ( ,
)
Check: sub the POI into both equations
Equation 1: y = 2x + 1
Equation 2: y = -x + 4
( ) = 2( ) + 1
Example 2: Which ordered pair is a solution to the given system of linear equations?
x+y=6
(-2,4) or (2,4)?
2x – y = 0
Required Practice: P60 #4, 5ac, 6ac, 9ace, 11
( ) =-( ) +4
Unit 1: Linear Systems
Date: ______________________
Example 3: Graph the following pairs of equations and find the point of intersection. Label your graphs. Verify that
the POI is correct.
1.
y
y
x 7
2.
y
x 3
y
3. 3x + y = 7
2x –3y = 12
1
x 5
3
2
x 2
3
4. 2 x 3 y 6 0
x 3y 3 0
Required Practice: P60 #4, 5ac, 6ac, 9ace, 11