March 06, 2012
Warm up
Solve each system using elimination.
3x - 2y = 3
-x + y = 1
10x - 9y = 46
-2x + 3y = 10
March 06, 2012
We have studied systems in this
chapter which have had one solution.
There are many systems that have an
infinite number of solutions or no
solution at all. In this section, we will
look at such systems and compare
them.
March 06, 2012
Inconsistent system:
A system which has no ordered pair that satisfies
both of the original equations.
-no common solutions exist
-lines are parallel
Consistent system:
A system which has one or more solutions.
-Independent system
•single, common solution
•lines intersect
-Dependent system
•infinite solutions
•graphing same lines
March 06, 2012
Solve this system.
x + 2y = 6
x + 2y = -4
(x + 2y = 6)-1
x + 2y = -4
-x - 2y = -6
x + 2y = -4
0 = -10
0 ≠ -10
This solution is never true,
therefore no solution exists.
The lines are parallel.
This is an inconsistent system.
March 06, 2012
2x - y = 1
x+y=5
2x - y = 1
x+y=5
3x = 6
3
3
x= 2
2+y=5
-2
-2
y =3
(2, 3)
This is an independent system,
one solution.
March 06, 2012
Solve
2y = -x - 4
2x = -4y - 8
1. Rewrite to standard form:
2y = -x - 4
+x +x
2x = -4y - 8
+4y +4y
2x + 4y = -8
x + 2y = -4
(x + 2y = -4)-2
2x + 4y = -8
-2x - 4y = 8
2x + 4y = -8
0=0
True, always.
Infinite number of solutions (all
terms subtracted out)
Dependent system
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Independent system
Dependent System
Inconsistent system
y = 2x - 3
2y = 4x - 6
y = 2x - 3
y = 2x + 4
y= x - 3
y = -2x + 3
different slopes
intersecting lines
one solution
same or different
y-intercept
· consistent
·
·
·
·
·
·
·
·
·
same slope
same line
infinite solutions
same y-intercept
consistent
·
·
·
·
·
same slope
parallel lines
no solution
different y-intecepts
inconsisten
March 06, 2012
Determine if the following systems are independent, dependent, or inconsistent.
Set 1:
Set 2:
Set 3:
y = 2x - 3
y = -3x + 2
x+y=4
3y = 6x - 9
y = 2x + 2
x+y=5