Let
x------> the biggest number
y------> the middle number
z------> the smallest number
we know that
[tex]x=2y[/tex] -------> equation [tex]1[/tex]
[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]
[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]
[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]
[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]
using a graph tool-----> to resolve the system of equations
see the attached figure
the solution is the point [tex](6,8)[/tex]
[tex]z=6\\y=8[/tex]
Find the value of x
[tex]x=2y[/tex]
[tex]x=2*8=16[/tex]
therefore
the answer is
the biggest number is [tex]16[/tex]
the the middle number is [tex]8[/tex]
the smallest number is [tex]6[/tex]
