Question

Question #a9fdf

Answer 1

`(2,3)" or " (3,2)`

Explanation:

Rearrange x + 5y in terms of x or y and substitute into xy = 6.

`x+y=5rArry=5-x`

substitute this into xy = 6

`rArrx(5-x)=6`

distribute and equate to zero.

`rArr5x-x^2=6rArrx^2-5x+6=0`

Factorising the quadratic gives.

`(x-2)(x-3)=0rArrx=2,x=3`

`x=2toy=5-2=3to(2,3)" is a solution"`

`x=3toy=5-3=2to(3,2)" is also a solution"`

This can be checked fairly ' easily' as follows.

`x=2,y=3rArrx+y=2+3=5" and " xy=2xx3=6`

`x=3,y=2rArrx+y=3+2=5" and " xy=3xx2=6`