Identify coefficients

Represent the equations in the standard form $a_1 x + b_1 y = c_1$ and $a_2 x + b_2 y = c_2$. Here, $a_1 = 5, b_1 = -3, c_1 = 7$ and $a_2 = 7, b_2 = 4, c_2 = 18$.

$a_1=5, b_1=-3, a_2=7, b_2=4$

Calculate the determinant (D)

For a system to have a unique solution, the determinant of the coefficient matrix must not be zero: $D = a_1 b_2 - a_2 b_1$.

$D = (5)(4) - (7)(-3) = 20 + 21 = 41$

Conclusion

Since the determinant $D = 41 \neq 0$, the lines are not parallel and must intersect at exactly one unique point.

$D \neq 0 \implies \text{Unique solution}$