Pair of Linear ...

$$A$$ is $$25$$ years older than $$B$$. In $$15$$ years, $$A$$ will be twice of $$B$$. Find the present ages of $$A$$ and $$B$$.

A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.

Find the fraction such that it becomes $$\displaystyle \frac{1}{2}$$ if 1 is added to the numerator, and $$\displaystyle \frac{1}{3}$$ if 1 is added to the denominator.

$$7x+6y= 71$$
$$5x-8y= -23$$

$$\displaystyle \frac{5y}{2}-\displaystyle \frac{x}{3}= 8$$
$$\displaystyle \frac{y}{2}+\displaystyle \frac{5x}{3}= 12$$

$$3x - 4y = 1$$ and $$x - 2y + 1 = 0$$

$$3x - 2y = 0$$ and $$y + 3 = 0$$

$$x + y = 0$$ and $$y = 5$$

Solve the following pair of linear (simultaneous) equations by the method of elimination :

Solve the following pairs of equations, graphically :