SOLUTION: x+2y=1 and 2x+5y=3

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Question 253263: x+2y=1 and 2x+5y=3
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%2B2y=1%2C2x%2B5y=3%29


-2%28x%2B2y%29=-2%281%29 Multiply the both sides of the first equation by -2.


-2x-4y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-2x-4y=-2%2C2x%2B5y=3%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:


%28-2x-4y%29%2B%282x%2B5y%29=%28-2%29%2B%283%29


%28-2x%2B2x%29%2B%28-4y%2B5y%29=-2%2B3 Group like terms.


0x%2By=1 Combine like terms.


y=1 Simplify.


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-2x-4y=-2 Now go back to the first equation.


-2x-4%281%29=-2 Plug in y=1.


-2x-4=-2 Multiply.


-2x=-2%2B4 Add 4 to both sides.


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


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


x=-1 Reduce.


So the solutions are x=-1 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 x%2B2y=1 (red) and 2x%2B5y=3 (green)