Forming Simultaneous Equations (Cambridge (CIE) O Level Maths): Revision Note

• Always check that you've answered the question! Sometimes finding x and y isn't the end

  • E.g. you may have to state a conclusion

At a bakery a customer pays £9 in total for six bagels and twelve sausage rolls.

Another customer buys nine bagels and ten sausage rolls, which costs £12.30 in total.

Find the cost of 5 bagels and 15 sausage rolls.

Answer:

The two variables are the price of bagels, $b$, and the price of sausage rolls, $s$

Write an equation for the first customer's purchases, and label it equation 1

$\overline{)1}6b+12s=9$

Write an equation for the second customer's purchases, and label it equation 2

$\overline{)2}9b+10s=12.3$

We will choose to eliminate the $b$ terms
Make the $b$ terms equal by multiplying all parts of equation 1 by 3 and all parts of equation 2 by 2
Label these as equations 3 and 4

$\begin{array}{rcl}\overline{)1}\times 318b+36s& =& 27\overline{)3}\\ \overline{)2}\times 218b+20s& =& 24.6\overline{)4}\end{array}$

To eliminate $b$, subtract equation 4 from equation 3

$\overline{)3}-\overline{)4}16s=2.4$

Solve for $s$

$s=\frac{2.4}{16}=0.15$

Substitute this into either equation to find $b$, we will use equation 1

$\begin{array}{rcl}\overline{)1}6b+12\left(0.15\right)& =& 9\\ 6b+1.8& =& 9\\ 6b& =& 7.2\\ b& =& 1.2\end{array}$

So sausage rolls cost £0.15 each and bagels cost £1.20 each

Use these values to find the price of 5 bagels and 15 sausage rolls

$\left(5\times 1.2\right)+\left(15\times 0.15\right)=8.25$

£8.25