Step-by-step explanation:
XY = 3WX
3WX - XY = 0
X(3W - Y) = 0
By zero product rule, either X = 0 or 3W = Y.
YZ = 6WX = 2XY (From 1st equation)
2XY - YZ = 0
Y(2X - Z) = 0
Again by zero product rule, either Y = 0 or 2X = Z.
Therefore, either both X and Z = 0, or both W and Y = 0. Let's look at the last equation.
WZ = 10WX
10WX - WZ = 0
W(10X - Z) = 0.
Here, either W = 0 or 10X - Z = 0.
- If both X and Z were 0, 10X - Z = 0.
- If both W and Y were 0 instead, W = 0.
Since both ways satisfy the equation, it is proved.
