If $7\mathrm{x}+8\mathrm{y}=53$ and $5\mathrm{x}+12\mathrm{y}=63$ , then what is the value of $\left(\mathrm{y}-\mathrm{x}\right)$ ?

Find $c$ if the system of equations $cx+3y+\left(3-c\right)=0$; $12x+cy-c=0$ has infinitely many solutions.

The solution set of the given pair of linear equation $5x-5y=-5$ and $\frac{3x}{2}-\frac{3y}{2}+\frac{3}{2}=0$ is _____.

Solve the following pair of equations  by reducing them to a pair of linear equation:

$\frac{10}{x+y}+\frac{2}{x-y}=4 ; \frac{15}{x+y}-\frac{5}{x-y}=-2$

Consider the following pairs of linear equation:

$$\begin{gathered} \left(i\right) 3x+2y=5 ; 2x+3y=5 \\ \left(ii\right) 2x-3y=7; 2x-3y=8 \end{gathered}$$

Choose the correct alternative.

The value of $‘x’$and $‘y’$ for the linear equations:

$a_{1}x + b_{1}y + c_1= 0$ and $a_{2}x + b_{2}y + c_2= 0$are

In Fig. 1, $ABCD$ is a rectangle. Find the values of $x$ and $y$.

Solve the following pair of equation by reducing them to a pair of linear equations:

$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$

$\frac{1}{2\left(3x+y\right)}-\frac{1}{2\left(3x-y\right)}=\frac{-1}{8}$