Question

the diagonals ac and bd of a parllelogram abcd intersect at o.if oa= 6-x,oc=y+4,ob=9-4x and od=2y-1,find the values of x and y

Answer 1

as we know that the diagonals of the parallelogram are equal so we get,
⇒diagonal oa=diagonal oc
6-x=y+4
x+y=6-4
x+y=2-----------equation 1
⇒diagonal ob=diagonal od
9-4x=2y-1
-4x-2y=-1-9
-4x-2y=-10
-2(2x+y)=-10
2x+y=5-----------equation 2

by subtracting the equation 1 and 2 we get,
2x+y-x-y=5-2
x=3
and by  substituting  equation 2 we get,
2(3)+y=5
6+y=5
y=-6+5
y=-1