Classifying Systems
Elimination
Substitution
SURPRISE
Any Method
100
y= (-4/3)x -2 *** y = (-4/3)x -1
INCONSISTENT
100
-10x + 9y = 19 *** 6x - 9y = -15
(-1, 1)
100
y = 2x - 14 *** y = -3x + 16
(6, -2)
100
y = (-1/3)x + 3 *** y = -2x - 2
(-3, 4)
100
9y + 6x = 3 *** -2x = -y + 3
(-1, 1)
200
y = -7x -3 *** y = -x + 3
INDEPENDENT
200
-3x + 4y = -12 *** -3x + 2y = -12
(4, 0)
200
y = 4x - 1 *** y = 8x - 5
(1, 3)
200
40x - 70y = 30 *** -16x + 28y = -12
Infinite Solutions/Dependent System
200
8y - 8x = 8 *** -9 - 27y = -15x
(-3, -2)
300
x - 4y = -8 *** x - 4y = 8
INCONSISTENT
300
-x + 8y = 2 *** 7x + y = -14
(-2, 0)
300
y = x + 1 *** 2x + 3y = -7
(-2, -1)
300
y = -7 *** -x - y = 1
(6, -7)
300
x = -2 - (1/2)y *** -40 = -18x + 10y
(0, -4)
400
-6 = -2y - 5x *** -2y - 5x = -6
DEPENDENT
400
-8x - 14y = -6 *** 5x + 7y = -5
(-8, 5)
400
x = 4 + y *** -8x + 4y = -20
(1, -3)
400
4x - 2y = 6 *** y = 2x - 3
Infinite Solutions/Dependent System
400
-y - (9/5) - (7/5)x = 0 *** -6y = 5x - 13
(-7, 8)
500
0 = -y + 4 + 2x *** x = 12 + 4y
INDEPENDENT
500
8x - 7y = 8 *** 3x - 5y = 22
(-6, -8)
500
-6x - 7y = 2 *** x = 3 + (1/2)y
(2, -2)
500
-4x - 3y + 5z = -28 *** -x + 3y + 3z = 5 *** -4x - 5y + 2z = -22
(-5, 6, -6)
500
10x = 9y + 28 *** (-7/18)y = 1 - (2/9)x
(1, -2)
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