SOLUTION: Can you pls help me solve the system? 2x+5y=1 -x+6y=8

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Question 227942: Can you pls help me solve the system?
2x+5y=1
-x+6y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%282x%2B5y=1%2C-x%2B6y=8%29


2%28-x%2B6y%29=2%288%29 Multiply the both sides of the second equation by 2.


-2x%2B12y=16 Distribute and multiply.


So we have the new system of equations:
system%282x%2B5y=1%2C-2x%2B12y=16%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%282x%2B5y%29%2B%28-2x%2B12y%29=%281%29%2B%2816%29


%282x%2B-2x%29%2B%285y%2B12y%29=1%2B16 Group like terms.


0x%2B17y=17 Combine like terms.


17y=17 Simplify.


y=%2817%29%2F%2817%29 Divide both sides by 17 to isolate y.


y=1 Reduce.


------------------------------------------------------------------


2x%2B5y=1 Now go back to the first equation.


2x%2B5%281%29=1 Plug in y=1.


2x%2B5=1 Multiply.


2x=1-5 Subtract 5 from both sides.


2x=-4 Combine like terms on the right side.


x=%28-4%29%2F%282%29 Divide both sides by 2 to isolate x.


x=-2 Reduce.


So the solutions are x=-2 and y=1.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x%2B5y=1 (red) and -x%2B6y=8 (green)