Pair of Linear ...

Solve the following pair of simultaneous equations:

Solve the following pair of simultaneous equations:

Solve the following pair of simultaneous equations:

Solve the following pair of simultaneous equations:

Find two numbers such that twice of the first added to the second gives $$21$$, and twice the second added to the first gives $$27$$.

A man's age is three times that of his son and in twelve years he will be twice as old as his son would be. What are their present ages?

Find two numbers whose sum is $$15$$ and difference is $$3$$.

Find a fraction which reduces to $$\displaystyle \frac{2}{3}$$ if the numerator and the denominator are each increased by $$1$$, and reduces to $$\displaystyle \frac{3}{5}$$ if the numerator and the denominator are each decreased by $$2$$.

Find two numbers, which differ by $$7$$, such that twice the greater added to five times the smaller gives $$42$$.