SOLUTION: 5. Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the a

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Question 144716: 5. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
x + 5y = 4
2x – 5y = 2


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!


Start with the given system of equations:






Multiply the top equation (both sides) by
Multiply the bottom equation (both sides) by




Distribute and multiply





Now add the equations together. In order to add 2 equations, group like terms and combine them



Combine like terms and simplify



Notice how the x terms cancel out




Simplify




Divide both sides by to isolate y




Reduce



Now plug this answer into the top equation to solve for x

Start with the first equation



Plug in




Multiply




Reduce



Subtract 2 from both sides


Combine like terms on the right side




So our answer is
and



which form the ordered pair




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