The problem was essentially a simple one using addition and algebra.

The solutions are:

(i)

(ii)

This gave a
= 19
+ 33 = 52 |

(iii)

All the solutions to this
came from the relationship x
+ y
= 2.The value of b
was 10. |

N.B. Allowing negative integers here, there are infinitely many
possible values for *x*
and *y*, but only one
possible value of *b*
.

(iv)

The relationship for
x
and y
is given as:x
+ 3 y
= 27. |

By choosing whole number values for *y*
, this
relationship will always give whole number values for *x*
.
Again here, allowing for negative integers , there are infinitely
many possible values for *x*
and *y*
.