On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

The cost of $2$ pencils and $3$ erasers is ₹ $9$,and the cost of $4$ pencils and $6$ erasers is ₹ $18$. Determine the cost of each pencil and each eraser.

$k$ ની કઈ કિંમત માટે નીચે આપેલ સુરેખ સમીકરણોની જોડને કોઈ ઉકેલ નથી?
$3x + y = 1$
$(2k - 1)x + (k - 1)y = 2k + 1$

Solve the following pair of linear equations:
$ax + by = c$
$bx + ay = 1 + c$

Form the pair of linear equations for the following problem,and find their solutions (if they exist) by the elimination method:
If we add $1$ to the numerator and subtract $1$ from the denominator,a fraction reduces to $1$. It becomes $\frac{1}{2}$ if we only add $1$ to the denominator. What is the fraction?

Let us take the example: Akhila goes to a fair with ₹ $20$ and wants to have rides on the Giant Wheel and play Hoopla. Represent this situation algebraically and graphically (geometrically).