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 an

Algebra ->  Linear-equations -> 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 an      Log On


   

Question 153565: . 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.”
5x – 4y = 1
-10x + 8y = -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%285x-4y=1%2C-10x%2B8y=-3%29


2%285x-4y%29=2%281%29 Multiply the both sides of the first equation by 2.


10x-8y=2 Distribute and multiply.


So we have the new system of equations:
system%2810x-8y=2%2C-10x%2B8y=-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:


%2810x-8y%29%2B%28-10x%2B8y%29=%282%29%2B%28-3%29


%2810x%2B-10x%29%2B%28-8y%2B8y%29=2%2B-3 Group like terms.


0x%2B0y=-1 Combine like terms. Notice how the x terms cancel out.


0=-1Simplify.


Since 0=-1 is never true, this means that there are no solutions. So the system is inconsistent.