Find out the value of x and y #3+x+xy=0# #2x+5y=8# ???
Thanks in advance !
Thanks in advance !
1 Answer
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]}