3.1 Solving Linear Systems by Graphing

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System of 2 linear equations (in 2 variables x & y)

• 2 equations with 2 variables (x & y) each.

Ax + By = C

Dx + Ey = F

• Solution of a System –

an ordered pair (x,y) that makes both eqns true.

Ex: Check whether the ordered pairs are solns. of the system.

x-3y= -5-2x+3y=10

A. (1,4)

1-3(4)= -5

1-12= -5

-11 = -5

*doesn’t work in the 1st eqn, no need to check the 2nd.

Not a solution.

B. (-5,0)

-5-3(0)= -5

-5 = -5

-2(-5)+3(0)=10

10=10

Solution

Solving a System GraphicallySolving a System Graphically

1. Graph each equation on the same coordinate plane. (USE GRAPH PAPER!!!)

2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution.

3. If the lines do not intersect:a. They are the same line – infinitely many

solutions (they have every point in common).

b. They are parallel lines – no solution (they share no common points).

Ex: Solve the system graphically.2x-2y= -82x+2y=4

(-1,3)

Ex: Solve the system graphically.2x+4y=12

x+2y=6• 1st eqn:

x-int (6,0)

y-int (0,3)• 2ND eqn:

x-int (6,0)

y-int (0,3)• What does this mean?

the 2 eqns are for the same line!

• ¸ many solutions

Ex: Solve graphically: x-y=5 2x-2y=9• 1st eqn:

x-int (5,0)

y-int (0,-5)• 2nd eqn:

x-int (9/2,0)

y-int (0,-9/2)• What do you notice

about the lines?• They are parallel! Go

ahead, check the slopes!• No solution!