7.1 solving linear systems by graphing systems of linear equations solving systems of equations by...

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!