Solve the following pair of equations by cross multiplication method.

$$\begin{gathered} 7x-y=23 \\ 8x+3y=18 \end{gathered}$$

Solve the following pair of equations by cross multiplication method.

$$\begin{gathered} 9x+5y=7 \\ 6x-y=22 \end{gathered}$$

Solve the following pair of equations by cross multiplication method.

$$\begin{gathered} 11x+5y=7 \\ 6x-3y=21 \end{gathered}$$

Solve the following pair of equations by cross multiplication method.

$$\begin{gathered} 2x-5y=14 \\ x+2y+2=0 \end{gathered}$$

The difference between two numbers is $4$ and six times the smaller is equal to four times the greater. Find the numbers.

The sum of two numbers is $48$ and five times the smaller number is equal to three times the greater number. Find the numbers.

Find two numbers such that the sum of thrice the first number and twice the second number is $102$. Also, five times the first number exceeds thrice the second number by $18$. Find the numbers.

Two numbers are in ratio $4:7$. If $4$ is subtracted from each of the numbers, then the ratio becomes $7:13$. Find the numbers.

Two numbers are in ratio $3:5$. If $5$ is added to each of the numbers, then the ratio becomes $2:3$. Find the numbers.