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Question 1205197: what is the answer to this elimination equation
5x-10y=-15
6x-5y=10
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Double both sides of 6x-5y=10 to get 12x-10y=20
The original system is equivalent to
5x-10y=-15
12x-10y=20
Subtract straight down
5x-12x becomes -7x
The y terms cancel
The right hand side values subtract to -15-20 = -35
We end up with -7x = -35 which solves to x = 5.
Use this x value to find y.
5x-10y=-15
5*5-10y=-15
25-10y=-15
-10y=-15-25
-10y=-40
y = -40/(-10)
y = 4
Answer: (x,y) = (5,4)
This system is consistent and independent.
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Confirming the answer:
If you use something like a TI83 to graph, then you should notice the two lines intersect at (5,4)
This is a quick visual way to confirm the answer. It's also a quick way to get the answer if you're short on time.
Alternative free graphing tools are Desmos or GeoGebra which in my opinion are arguably much better than a TI83. But for exam purposes, the TI83 (or similar) is the more standard option.
Another way to confirm the answer is to plug those coordinates into each of the original equations.
If we do so with the 1st equation we get
5x-10y=-15
5*5-10*4=-15
25-40 = -15
-15 = -15
Then do so with the 2nd equation
6x-5y=10
6*5-5*4=10
30-20 = 10
10 = 10
Both equations are true when we plugged in (x,y) = (5,4), so we have confirmed the answer is correct.
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