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

6­1 Solving Systems Using Graphs

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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)

6­1 Solving Systems Using Graphs

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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

6­1 Solving Systems Using Graphs

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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