If (64) x =(48) y =(36) z then show that 1/x +1/z = 2/y
64x = 48y = 36z
Three equations:
64x = 48y
48y = 36z
1/x + 1/z = 2/y
The third equation is true if solving this system of equations results in an "always true" statement like 2 = 2 or 37 = 37.
64x = 48y
48y = 36z
1/x + 1/z = 2/y
divide the first equation by 64 on both sides and the second equation by 36 on both sides
x = (48/64)y
(48/36)y = z
1/x + 1/z = 2/y
simplify
x = (3/4)y = 3y/4
z = (4/3)y = 4y/3
1/x + 1/z = 2/y
plug the x and z values from the first and second equation into the third equation:
1/(3y/4) + 1/(4y/3) = 2/y
solve
4/(3y) + 3/(4y) = 2/y
multiply both sides by 12y
16 + 9 = 24
25 = 24
This is never true, so if (64) x =(48) y =(36) z then 1/x +1/z does not equal 2/y.