Transcript 3.1 Solving Linear Systems by Graphing

7.1 Solving Linear Systems by
Graphing
•Systems of Linear Equations
•Solving Systems of Equations by Graphing
Introduction to System of 2
linear equations
To solve a linear system by graphing
________ first graph
intersection
each equation separately. Next identify the __________
of both lines and circle it. That ordered pair is the
solution
_______ to the system. Check your answer by plugging it
system of equations.
back into the ______
Solving 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).
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)= -5
1-12= -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)=10
10=10
Solution
Example: Solve the system graphically.
2x-2y= -8
2x+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!
Assignment:
• Complete 6, E, and F on the note taking guide!