One says, "Give me a hundred, friend! I shall then become twice as rich as you" the other replies, "If you give me ten, I should be six times as rich as you." Tell me what is the amount of their (respective) capitals?

Once a mule and a donkey were talking. The mule said, "I am carrying more sacks than you. In fact, if you give me one of your sacks, then I would have twice as many as you. If I give a sack, our loads would be equal." How many sacks was each animal carrying?

The sum of the numerator and denominator of a fraction is $3$ less than twice the denominator. If the numerator and denominator are decreased by $1$, the numerator becomes half the denominator. Determine the fraction.

Solve the following pairs of linear equations by the elimination method:

$$\begin{gathered} 3x+4y=10 \\ 2x-2y=2 \end{gathered}$$

Solve the following pairs of linear equations by the elimination method:

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

Solve the following pairs of linear equations:

$$\begin{gathered} \frac{x+1}{2}+\frac{y-1}{3}=8 \\ \frac{x-1}{3}+\frac{y+1}{2}=9 \end{gathered}$$

Solve the following pairs of linear equations:

$$\begin{gathered} x+\frac{6}{y}=6 \\ 3x-\frac{8}{y}=5 \end{gathered}$$

Solve the following pairs of linear equations by the elimination method:

$$\begin{gathered} px+qy=p-q \\ qx-py=p+q \end{gathered}$$

Solve the following pair of linear equations by the elimination method:

$$\begin{gathered} \frac{x}{a}-\frac{y}{b}=0 \\ ax+by=a^2+b^2 \end{gathered}$$