Question

Solve the equation.
2x-3y-5z=-16

x __ __ __
y = __ + __ s + __ t
z __ __ __

Answer 1

Well you have a single equation in three unknowns, so that means you can express one variable in terms of the other two. The suggestion seems to indicate expressing y in terms of x and z. So we have to re-arrange this\[2x - 3y -5z = -16\]to bring y by itself on, say, the LHS :\[-3y = -16 -2x +5z\]\[y= (-16)(-3)-2x/(-3)+5z/(-3)\]thus\[y = 16/3 + (2/3)x+(-5/3)z\]giving the final form of answer as :\[x = s\]\[y =16/3 + (2/3)s+(-5/3)t \]\[z=t\]