Mathematics

These two equations represent lines in the plane, and a unique solution exists only when the lines intersect at exactly one point. Notice that the second equation's left side is almost exactly twice the first—the coefficients of $x$ and $y$ follow the pattern $4 = 2(2)$ and $6 = 2(3)$. This means the lines are parallel (same slope), but the constant terms don't follow this doubling pattern ($1 \neq 2(5)$), so they're distinct parallel lines that never meet. No intersection means no solution.

These two equations represent lines in the plane, and a unique solution exists only when the lines intersect at exactly one point. Notice that the second equation's left side is almost exactly twice the first—the coefficients of $x$ and $y$ follow the pattern $4 = 2(2)$ and $6 = 2(3)$. This means the lines are parallel (same slope), but the constant terms don't follow this doubling pattern ($1 \neq 2(5)$), so they're distinct parallel lines that never meet. No intersection means no solution.