Find the values of x and y if

Solution:

Here,

$x+10=3 x+4 \quad[\because$ All the corresponding elements of the matrix are equal $]$

$\Rightarrow x-3 x=4-10$

$\Rightarrow-2 x=-6$

$\therefore x=3$

Also,

$y^{2}+2 y=3$

$\Rightarrow y^{2}+2 y-3=0$

$\Rightarrow y^{2}+3 y-y-3=0$

$\Rightarrow y(y+3)-1(y+3)=0$

$\Rightarrow(y+3)(y-1)=0$

$\Rightarrow y+3=0$ or $y-1=0$

$\Rightarrow y=-3$ or $y=1$

Now,

$-4=y^{2}-5 y$

$\Rightarrow y^{2}-5 y+4=0$

$\Rightarrow y^{2}-4 y-y+4=0$

$\Rightarrow y(y-4)-1(y-4)=0$

$\Rightarrow(y-4)(y-1)=0$

$\Rightarrow y-4=0$ or $y-1=0$

$\Rightarrow y=4$ or $y=1$

Since $y^{2}+2 y=3$ and $y^{2}-5 y=-4$ must hold good simultaneously, we take the common solution of these two equations.

Thus,

$y=1, x=3$ and $y=1$