Transcript 3.1 Solving Linear Systems by Graphing p. 139 System of 2 linear equations (in 2 variables x & y) • 2 equations with 2

3.1 Solving Linear Systems by
Graphing
p. 139
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 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= -8
2x+2y=4
(-1,3)
Ex: Solve the system graphically.
2x+4y=12
x+2y=6
st
• 1 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
1st eqn:
2x-2y=9
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!
Assignment