If $2x + y = 35$ and $3x + 4y = 65$,then find $\frac{x}{y}$.

Susan invested a certain amount of money in two schemes $A$ and $B,$ which offer interest at the rate of $8 \%$ per annum and $9 \%$ per annum,respectively. She received $Rs.\, 1860$ as annual interest. However,had she interchanged the amount of investments in the two schemes,she would have received $Rs.\, 20$ more as annual interest. How much money did she invest in each scheme?

Solve the following pair of linear equations by the method of substitution: $x + 11y = 1$ and $8x + 13y = 2$.

The sum of the digits of a two-digit number is $9$. The number obtained by interchanging the digits exceeds the original number by $45$. Find the original number.

The solution set of the pair of equations $x+y+1=0$ and $3x+3y+2=0$ is .........

The pair of equations $x=a$ and $y=b$ graphically represents lines which are