Question

Solve for y : $\left|\begin{array}{ccc}x+y& x& x\\ x& x+y& x\\ x& x& x+y\end{array}\right|=16(3x+4)$

Answer 1

$\left|\begin{array}{ccc}x+y& x& x\\ x& x+y& x\\ x& x& x+y\end{array}\right|=16(3x+y)$

$row2=row2-row3$

$⟹\left|\begin{array}{ccc}x+y& x& x\\ 0& y& -y\\ x& x& x+y\end{array}\right|=16(3x+y)$

$row3=row3-row1$

$⟹\left|\begin{array}{ccc}x+y& x& x\\ 0& y& -y\\ -y& 0& y\end{array}\right|=16(3x+y)$

$⟹(x+y)\left(y^2\right)-y(-xy-xy)=16(3x+y)$

$⟹x{y}^2+y^3+2x{y}^2=16(3x+y)$

$⟹y^3+3x{y}^2=16(3x+y)$

$⟹y^2(y+3x)=16(3x+y)$

$⟹y^2=16$

$⟹y=4$