7.1 Solving Linear Systems by Graphing

•Systems of Linear Equations•Solving Systems of Equations by Graphing

To solve a linear system by ________ first graph each equation separately. Next identify the __________ of both lines and circle it. That ordered pair is the _______ to the system. Check your answer by plugging it back into the ______ of equations.

graphingintersection

solutionsystem

Introduction to System of 2 linear equations

Solving a System Solving a System GraphicallyGraphically

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).

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 equations true.

Example: Check whether the ordered pairs are solutions of the system.

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

A. (1,4)1-3(4)= -51-12= -5-11 = -5*doesn’t work in the 1st

equation, no need to check the 2nd.

Not a solution.

B. (-5,0)-5-3(0)= -5-5 = -5

-2(-5)+3(0)=1010=10

Solution

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

(-1,3)

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

x+2y=6• 1st equation:

x-int (6,0)y-int (0,3)

• 2ND equation:x-int (6,0)y-int (0,3)

• What does this mean?The 2 equations are for the same line!

• many solutions

Example: Solve graphically: x-y=5 2x-2y=9• 1st equation:

x-int (5,0)y-int (0,-5)

• 2nd equation: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!

AssignmentAssignment::

• Complete 6, E, and F on the note taking guide!