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Simple Substitution
Substition (distribution)
Substitution
(One given variable)
substitution (solving for a variable)
elimination
100
x + y = 8............ y = 3x
(2,6)
100
-2x +5y = 19.......... 3x - 4 = y
(3,5)
100
y = -2........ 4x -3y = 18
(3,-2)
100
y = 2x + 1........... 4x - 2y = 6
no solution
100
2x + 5y = 17......... 6x - 5y = -9
(1,3)
200
2x + 2y = 10............. y = 4x
(1,4)
200
6 + 4x = y.......... -5x - y = 21
(-3,-6)
200
y = 5 5x - 2y = 15
(5,5)
200
y - 2x = 3......... 3x - 2y = 5
(-11, -19)
200
3x - 2y = 0........... 4x + 2y = 14
(2,3)
300
y = 3x........... x + y = -32
(-8, -24)
300
y = 5x - 7.......... -3x - 2y = -12
(2,3)
300
y = 8 - x.......... - 5 = y
(13,-5)
300
4x = 3y - 2............ 18 = 3x + y
(4,6)
300
5x - y = 0........... 3x + y = 24
(3,15)
400
3x - y = 10......... x = 2y
(4,2)
400
-2 + 5x = y.......... -3x + 6y =-12
(0,-2)
400
x = 3........... 2y + x = 3
(3,0)
400
2x + 2y = 38.......... y = x + 3
(8,11)
400
3x + 2y = -15.......... x - 2y = 19
(1,-9)
500
5x - 2y = 15.......... y = 2x
(15,30)
500
y = 5x - 3........... 3x - 8y = 24
(0,-3)
500
x = 5.......... y - 4 = 3x
(5,19)
500
x + y = 4.......... 3x + 3y = 12
infinitely many solutions
500
6x - 2y = 22............. -6x + 5y = -37
(2,-5)