Question

10. 2x + 3y = 5, xy = 1 answer is (x=3/2,y=2/3)
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Answer 1

Answer:

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

Algebra.Com

Question 983956: Solve

2x+3y=5

xy=1

Answer by josmiceli(19441) (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+