Find out the value of x and y 3+x+xy=0 2x+5y=8 ???

Thanks in advance !

1 Answer
Oct 12, 2017

(-1,2),(15/2,-7/5)

Explanation:

3+x+xy=0to(1)

2x+5y=8to(2)

"rearrange equation "(2)" in terms of x or y"

rArrx=1/2(8-5y)=4-5/2yto(3)

"substitute "x=4-5/2y" in "(1)

rArr3+4-5/2y+4y-5/2y^2=0

rArr-5/2y^2+3/2y+7=0

"multiply through by "-2

rArr5y^2-3y-14=0

rArr5y^2-10y+7y-14=0larr" split middle term"

"factorise by grouping"

color(red)(5y)(y-2)color(red)(+7)(y-2)=0

"factor out "(y-2)

rArr(y-2)(5y+7)=0

"equate each factor to zero and solve for y"

y-2=0rArry=2

5y+7=0rArry=-7/5

"substitute these values into equation "(3)
"for corresponding values of x"

y=2tox=4-5=-1

y=-7/5tox=4+7/2=15/2

rArr"points of intersection "(-1,2)" and "(15/2,-7/5)
graph{(3+x+xy)(y+2/5x-8/5)((x+1)^2+(y-2)^2-0.04)((x-15/2)^2+(y+7/5)^2-0.04)=0 [-10, 10, -5, 5]}