Pair of Linear Equations in Two Variables question bank (Maths)

Form the pair of linear equations in the following problems,and find their solutions graphically.
$5$ pencils and $7$ pens together cost ₹ $50$,whereas $7$ pencils and $5$ pens together cost ₹ $46$. Find the cost of one pencil and that of one pen.

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel,or are coincident:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$