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

Thanks in advance !

1 Answer
Jim G.
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]}

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