61 Solving Systems Using Graphs
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6-1 Solving Systems Using Graphs
Prior Knowledge: At what point do each pair of lines intersect?
A) B)
C) D)
(o, 4)(3, -1)
(-4, 2) No Solution
Don't C
opy
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The solution to a system of equations is the intersection point of the graphs.
(4, 2) is the solution.Don
't Cop
y
Use algebra to solve, then graphing technology to check. x + y = 1
‑x + 3y = 3(0, 1)
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2x ‑ 3y = ‑9
‑x ‑ y = 2(-3, 1)
Use algebra to solve, then graphing technology to check.
*Check to see if the given point is a solution to the system of equations.
Point: (‑4, 1)
‑4x + 3y = 19
5x ‑ 7y = ‑27
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*What is the solution to this system of equations?
This system is represented by the equations:
2x + y = 3
‑2x ‑ y = 4
~ Exactly One Solution
The intersection point (x,y)
~ No Solution
No solution
~ Infinitely Many Solutions
Infinite Solutions
No Intersection Parallel Lines
the same line get y alone2x + 2y=4 y=-x+2
POSSIBLE NUMBER OF SOLUTIONS