SOLUTION: Use elimination method in solving this;tnx x+3y=5 2x+y=5

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Question 183262: Use elimination method in solving this;tnx
x+3y=5
2x+y=5
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%2B3y=5%2C2x%2By=5%29


-2%28x%2B3y%29=-2%285%29 Multiply the both sides of the first equation by -2.


-2x-6y=-10 Distribute and multiply.


So we have the new system of equations:
system%28-2x-6y=-10%2C2x%2By=5%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-6y%29%2B%282x%2By%29=%28-10%29%2B%285%29


%28-2x%2B2x%29%2B%28-6y%2B1y%29=-10%2B5 Group like terms.


0x%2B-5y=-5 Combine like terms.


-5y=-5 Simplify.


y=%28-5%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=1 Reduce.


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-2x-6y=-10 Now go back to the first equation.


-2x-6%281%29=-10 Plug in y=1.


-2x-6=-10 Multiply.


-2x=-10%2B6 Add 6 to both sides.


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


x=%28-4%29%2F%28-2%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 x%2B3y=5 (red) and 2x%2By=5 (green)