SOLUTION: can you show me the correct formula for x+5y=13 -2x+4y=16

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Question 240551: can you show me the correct formula for x+5y=13
-2x+4y=16
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%28x%2B5y=13%2C-2x%2B4y=16%29


2%28x%2B5y%29=2%2813%29 Multiply the both sides of the first equation by 2.


2x%2B10y=26 Distribute and multiply.


So we have the new system of equations:
system%282x%2B10y=26%2C-2x%2B4y=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%2B10y%29%2B%28-2x%2B4y%29=%2826%29%2B%2816%29


%282x%2B-2x%29%2B%2810y%2B4y%29=26%2B16 Group like terms.


0x%2B14y=42 Combine like terms.


14y=42 Simplify.


y=%2842%29%2F%2814%29 Divide both sides by 14 to isolate y.


y=3 Reduce.


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2x%2B10y=26 Now go back to the first equation.


2x%2B10%283%29=26 Plug in y=3.


2x%2B30=26 Multiply.


2x=26-30 Subtract 30 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=3.


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 x%2B5y=13 (red) and -2x%2B4y=16 (green)