Question 1194066
<font color=black size=3>
We have a 2 by 2 matrix on the left hand side. We are applying the determinant to it because of the vertical bars.


The determinant of 
{{{(matrix(2,2,a,b,c,d))}}}
is
{{{ad-bc}}}
This only works for 2 by 2 matrices.
We compute the product of the diagonals, then subtract those products.


In the case of 
{{{(matrix(2,2,3x,x,16x,x))}}} 
the determinant is
{{{ad - bc = 3x*x - x*16x = 3x^2 - 16x^2 = -13x^2}}}


Set this equal to the 35 and solve for x.
{{{-13x^2 = 35}}}


{{{x^2 = 35/(-13)}}}


{{{x = sqrt(-35/13)}}} or {{{x = -sqrt(-35/13)}}}


{{{x = i*sqrt(35/13)}}} or {{{x = -i*sqrt(35/13)}}}


We see that the solution set consists of nonreal complex numbers of the form a+bi, where {{{i = sqrt(-1)}}}


If your teacher has not covered imaginary numbers or complex numbers just yet, then the answer would be "no real solutions".
</font>