SOLUTION: Solve the equations for x and y or state that
there is no solution.
5x - 4y = 2
4x - 5y = -1
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
Multiply the both sides of the first equation by 4.
Distribute and multiply.
Multiply the both sides of the second equation by -5.
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 .
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Multiply EVERY term by the LCD to clear any fractions.
Distribute and multiply.
Add to 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.
Answer by stanbon(75887) (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.
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