In this worksheet, we look at **equations** with two unknowns.

* a *and

*stand for two numbers, which could be different or the same.*

**b**

Look at this equation.

**a + 2b = 8**

It tells you that * a added to double b is 8*.

If * a is 6, then b will be 1* because 6 + 2 × 1 = 6 + 2 = 8.

If * a = 2, then b = 3 *because 2 + 2 × 3 = 2 + 6 = 8.

If * a = 9*, then b must be negative.

*will be*

**b****because 9 + 2 × -½ = 9 + -1 = 8.**

*-½*If * a = 1, then b = 3½ *because 1 + 2 × 3½ = 1 + 7 = 8.

**Example**

**3a - 2b = 7**

Which of these solutions satisfy the equation?

a = 7, b = 0

a = 7, b = 7

a = 4, b = 2½

a = 5, b = 3

**Answer**

Put the given pairs into the equation to see if * 3a - 2b is 7* or not.

In each case, we work out * 3 × a take away 2 × b *to see if the answer is 7 or not.

a = 7, b = 0 | does not fit because 3 × 7 - 2 × 0 = 21 - 0 = 21 (not 7) |

a = 7, b = 7 | fits because 3 × 7 - 2 × 7 = 21 - 14 = 7 |

a = 4, b = 2½ | fits because 3 × 4 - 2 × 2½ = 12 - 5 = 7 |

a = 5, b = 3 | does not fit because 3 × 5 - 2 × 3 = 15 - 6 = 9 (not 7) |