Write a pair of linear equations which has the unique solution $x = -1, y = 3$. How many such pairs can you write?

(N/A) pair of linear equations in two variables is given by:
$a_1x + b_1y + c_1 = 0$
$a_2x + b_2y + c_2 = 0$
For the system to have a unique solution,the condition is $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.
Given the solution $x = -1$ and $y = 3$,these values must satisfy both equations:
$1$) $a_1(-1) + b_1(3) + c_1 = 0 \Rightarrow -a_1 + 3b_1 + c_1 = 0$
$2$) $a_2(-1) + b_2(3) + c_2 = 0 \Rightarrow -a_2 + 3b_2 + c_2 = 0$
We can choose arbitrary values for the coefficients that satisfy these conditions. For example,let $a_1 = 1, b_1 = 1$. Then $-1 + 3(1) + c_1 = 0 \Rightarrow c_1 = -2$. So,$x + y - 2 = 0$.
Let $a_2 = 1, b_2 = 2$. Then $-1 + 3(2) + c_2 = 0 \Rightarrow -1 + 6 + c_2 = 0 \Rightarrow c_2 = -5$. So,$x + 2y - 5 = 0$.
Since there are infinitely many combinations of $a_1, b_1, c_1$ and $a_2, b_2, c_2$ that satisfy the given solution and the condition for a unique solution,we can write infinitely many such pairs.