SOLUTION: Could someone look at my work and tell me what I'm doing wrong. Solve the system: {{{ ( 2 / x ) + ( 3 / 2y ) = ( 11/4 ) }}} {{{ (5 / 2x ) - ( 2 / y ) = ( 3 / 2 ) }}} --------

Algebra ->  Systems-of-equations -> SOLUTION: Could someone look at my work and tell me what I'm doing wrong. Solve the system: {{{ ( 2 / x ) + ( 3 / 2y ) = ( 11/4 ) }}} {{{ (5 / 2x ) - ( 2 / y ) = ( 3 / 2 ) }}} --------      Log On


   



Question 1007667: Could someone look at my work and tell me what I'm doing wrong.
Solve the system:
+%28+2+%2F+x+%29+%2B+%28+3+%2F+2y+%29+=+%28+11%2F4+%29+
+%285+%2F+2x+%29+-+%28+2+%2F+y+%29+=+%28+3+%2F+2+%29+
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I started by letting +a+=+%28+1+%2F+x+%29+ and +b+=+%28+1+%2F+y+%29+.
So:
= +%28+2a+%29+%2B+%28+3+%2F+2+%29b+=+%28+11%2F4+%29+
= +%285+%2F+2+%29a+-+%28+2b+%29+=+%28+3+%2F+2+%29+
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Then I got rid of the denominators on the right side of the '=' through multiplication
So:
= +%28+8a+%29+%2B+%28+6b+%29+=+%28+11+%29+
= +%285a+%29+-+%28+4b+%29+=+%28+3+%29+
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Then I got rid of the denominators that were on the left side of the '='
So:
= +%28+16a+%29+%2B+%28+12b+%29+=+%28+22+%29+
= +%2810a+%29+-+%28+8b+%29+=+%28+6+%29+
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Then I added the two together and solved for a.
= +26a+=+28+
= +a+=+%2828%2F26%29+
= +a+=+%2814%2F13%29+
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I then substituted what I found for a into the +%28+8a+%29+%2B+%28+6b+%29+=+%28+11+%29+ equation.
So:
= +8%28+14%2F13+%29+%2B+%28+6b+%29+=+%28+11+%29+
= +%28+112%2F13+%29+%2B+%28+6b+%29+=+%28+11+%29+
= +%28+6b+%29+=+%28+31%2F13+%29+
= +b+=+%28+31%2F78+%29+
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I then converted back to x and y.
+x+=+%28+1+%2F+a+%29+ = +13+%2F+14+
+y+=+%28+1+%2F+b+%29+ = +78+%2F+31+
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When I plug the x and y values back into the original equation, the x value works perfectly. However, I'm having a tough time getting the y value to match up.
What am I doing wrong?
Thank you for all your help!

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!


Solve the system:
+%28+2+%2F+x+%29+%2B+%28+3+%2F+2y+%29+=+%28+11%2F4+%29+
+%285+%2F+2x+%29+-+%28+2+%2F+y+%29+=+%28+3+%2F+2+%29+
------------------------------------------
------------------------------------------
I started by letting +a+=+%28+1+%2F+x+%29+ and +b+=+%28+1+%2F+y+%29+.
So:
= +%28+2a+%29+%2B+%28+3+%2F+2+%29b+=+%28+11%2F4+%29+
= +%285+%2F+2+%29a+-+%28+2b+%29+=+%28+3+%2F+2+%29+
------------------------------------------
Then I got rid of the denominators on the right side of the '=' through multiplication
So:
= +%28+8a+%29+%2B+%28+6b+%29+=+%28+11+%29+
= +%285a+%29+-+%28+4b+%29+=+%28+3+%29+
------------------------------------------
Then I got rid of the denominators that were on the left side of the '='
So:
= +%28+16a+%29+%2B+%28+12b+%29+=+%28+22+%29+
= +%2810a+%29+-+%28+8b+%29+=+%28+6+%29+
------------------------------------------

Above, b does not cancel off by adding the two equations
you have to eliminate b
= +%28+8a+%29+%2B+%28+6b+%29+=+%28+11+%29+ * 2
= +%285a+%29+-+%28+4b+%29+=+%28+3+%29+ ^ 3
we get
16a+12b = 22
15a -12b = 9
_____________

add
31a = 31
a= 1
Plug a
so we get b = 1/2
a= 1/x = 1 so x=1
b = 1/2 =`1/y
y=2
+%28+2+%2F+x+%29+%2B+%28+3+%2F+2y+%29+=+%28+11%2F4+%29+
%282%2F1%29%2B%283%2F4%29+
2%2B%283%2F4%29
11%2F4