SOLUTION: 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 answe
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Question 180714: 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" and state how you arrived at that conclusion.
4x + 10y = 2
3x + 5y = 5
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
Multiply the both sides of the second equation by -2.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So the solutions are and
Which form the ordered pair )
.
This means that the system is consistent and independent.
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