Graphing Systems of Equations
Substitution
Elimination Using Addition
Elimination Using Subtration
Elimination Using Multiplication
100
Definition: contains 2 equations
What is system of equations
100
y = x + 5 3x + y = 25
What is (5, 10)
100
8x + 5y = 38 -8x + 2y = 4
What is (1 , 6)
100
5m - p = 7 7m - p = 11
What is (2 , 3)
100
5x + 6y = -8 2x + 3y = -5
What is ( 2 , -3)
200
Definition: if a system has at least one solution it is said to be....(contains a solution)
What is consistent
200
y = 5x + 1 4x + y = 10
What is (1, 6)
200
-v + w = 7 v + w = 1
What is (-3 , 4)
200
-v + w = 7 v + w = 1
What is ( -3 , 4)
200
2x - y = 4 7x + 3y = 27
What is ( 3 , 2)
300
Definition: if the system contains exactly 1 solution
What is independent, in a consistent system.
300
x = y - 2 4x + y = 2
What is (0, 2)
300
-4x + 5y = 17 4x + 6y = -6
What is (-3 , 1)
300
y + z = 4 y - z = 8
What is ( 6 , -2)
300
2x + 7y = 1 x + 5y = 2
What is ( -3, 1)
400
Definition: If a system contains an infinite number of solutions (appears as the same line)
What is dependent, in a consistent system.
400
x - y = 1 3x = 3y + 3
What is infinitely many
400
5m - 2p = 24 3m + 2p = 24
What is (6 , 3)
400
a + 4b = -4 a + 10b = -16
What is ( 4 , -2)
400
4x + 2y = -14 5x + 3y = -17
What is ( -4, 1)
500
Definition: Is a system has no solution, the graphs are parallel
What is inconsistent
500
2x + 3y = 4 4x + 6y = 9
What is no solution
500
9x + 6y = 78 3x - 6y = -30
What is (4 , 7)
500
11f + 14g = 13 11f + 10g = 25
What is ( 5 , -3)
500
9a - 2b = -8 -7a + 3b = 12
What is ( 0, 4)
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