Graphically Speaking
Graphically Speaking
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Adding Methods in Special Cases?
Here is an example:
2x - 4y = 8
6x - 12y = 10
To solve this system, you would multiply the first equation by a -3 to make the x-values add out.
-3(2x - 4y) = -3(8) becomes -6x + 12y = -24
Put this new equation back with the second equation and then add the equations together.
-6x + 12y = -24
6x - 12y = 10
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0 = -14
Notice how both the x-values and the y-values added out here. This leaves us with an equation that says 0 = -14. Is that true? Does zero equal negative fourteen? Of course not.
When this situation happens, we say there is "no solution." Graphically speaking these lines have the same slope and would be parallel.
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What I'm not understanding with this example is, why pick -3 to make the x-values add-out? Could anyone provide me with assistance?
Maybe, you may consider the following method:
y in terms of x—1st & 2nd equations:
2x - 4y = 8
x - 2y = 4
2y = x - 4
y = (x - 4)/2
6x - 12y = 10
3x - 6y = 5
6y = 3x - 5
y = (3x - 5)/6
Value of x:
6(x - 4) = 2(3x - 5)
3(x - 4) = 3x - 5
3x - 12 = 3x - 5
0 = 7 IS FALSE
Answer: This problem has no solution. Something is wrong with one or both equations.
Discussion
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