SOLUTION: Solve 2x+3y=5 xy=1

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Question 983956: Solve
2x+3y=5
xy=1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2Ay+=+1+
+y+=+1%2Fx+
by substitution:
+2x+%2B+3%2A%281%2Fx%29+=+5+
+2x%5E2+%2B+3+=+5x+
+2x%5E2+-+5x+%2B+3+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-5+
+c+=+3+
+x+=+%28+-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A2%2A3+%29%29+%2F+%282%2A2%29+
+x+=+%28+5+%2B-+sqrt%28+25+-+24+%29%29+%2F+4+
+x+=+%28+5+%2B+1+%29+%2F+4+
+x+=+3%2F2+
and
+x+=+%28+5+-+1+%29+%2F+4+
+x+=+1+
----------------------
and
+y+=+1%2Fx+
+y+=+2%2F3+
and
+y+=+1+
---------------
The solutions are:
( 3/2, 2/3 ) and ( 1,1 )
----------------------
check:
+2x+%2B+3y+=+5+
+2%2A%283%2F2%29+%2B+3%2A%282%2F3%29+=+5+
+3+%2B+2+=+5+
+5+=+5+
OK
+2x+%2B+3y+=+5+
+2%2A1+%2B+3%2A1+=+5+
+2+%2B+3+=+5+
+5+=+5+
OK