Identify proportionality

Observe that the coefficients of the second equation are exactly twice those of the first: $4 = 2\times2$, $6 = 2\times3$, $16 = 2\times8$.

$4 = 2\times2, \; 6 = 2\times3, \; 16 = 2\times8$

Compute determinant

For a system $ax+by=c$ and $dx+ey=f$, the determinant $\Delta = ae - bd$ tells if the lines are parallel ($\Delta=0$) or intersecting ($\Delta \neq 0$). Here $a=2$, $b=3$, $d=4$, $e=6$.

$\Delta = 2\times6 - 3\times4 = 12 - 12 = 0$

Conclude nature of solutions

Since $\Delta = 0$ and the constant terms are also in the same ratio (16 = 2×8), the equations represent the same line, giving infinitely many solutions.

$\text{Infinite solutions because the equations are dependent}$