SOLUTION: Solve the equations for x and y or state that there is no solution. 5x - 4y = 2 4x - 5y = -1

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Question 183045: Solve the equations for x and y or state that
there is no solution.
5x - 4y = 2
4x - 5y = -1
Found 2 solutions by jim_thompson5910, stanbon:
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=2%2C4x-5y=-1%29


4%285x-4y%29=4%282%29 Multiply the both sides of the first equation by 4.


20x-16y=8 Distribute and multiply.


-5%284x-5y%29=-5%28-1%29 Multiply the both sides of the second equation by -5.


-20x%2B25y=5 Distribute and multiply.


So we have the new system of equations:
system%2820x-16y=8%2C-20x%2B25y=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:


%2820x-16y%29%2B%28-20x%2B25y%29=%288%29%2B%285%29


%2820x%2B-20x%29%2B%28-16y%2B25y%29=8%2B5 Group like terms.


0x%2B9y=13 Combine like terms.


9y=13 Simplify.


y=%2813%29%2F%289%29 Divide both sides by 9 to isolate y.


------------------------------------------------------------------


20x-16y=8 Now go back to the first equation.


20x-16%2813%2F9%29=8 Plug in y=13%2F9.


20x-208%2F9=8 Multiply.


9%2820x%29-cross%289%29%28208%2Fcross%289%29%29=9%288%29 Multiply EVERY term by the LCD 9 to clear any fractions.


180x-208=72 Distribute and multiply.


180x=72%2B208 Add 208 to both sides.


180x=280 Combine like terms on the right side.


x=%28280%29%2F%28180%29 Divide both sides by 180 to isolate x.


x=14%2F9 Reduce.


So the solutions are x=14%2F9 and y=13%2F9.


Which form the ordered pair .


This means that the system is consistent and independent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
5x - 4y = 2
4x - 5y = -1
---------------------
Multiply 1st thru by 4 and 2nd thru by 5 to get:
---------------
20x - 16y = 8
20x - 25y = -5
--------------------
Subtract 2nd from 1st to get:
9y = 13
y = 13/9
------------
Substitute into 4x - 5y = -1 to solve for "x":
4x - 5(13/9) = -1
36x - 65 = -9
36x = 56
x = 14/9
-----------------
x = 14/9 ; y = 13/9
=========================
Cheers,
Stan H.