Year 11 Maths - Methods Reviewing Linear Equations

Constructing Simultaneous Linear Equations

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Questions

Question 1

17333

The sum of two numbers is \({\rm{72}}\), and their difference is \({\rm{40}}\). The numbers are?

Answer

\(56\) and \(16\)

Worked Solution

\begin{align}
&\text { Let } x \text { be the larger number and } y \text { the smaller. } \\
&\qquad \begin{aligned}
x+y &=72\cdots (1)\\
x-y &=40\cdots (2) \\
(1)+(2)\qquad 2x&=112 \rightarrow x=56 \\
\end{aligned}\\
& \text{In } (1)\quad 56+y=72 \rightarrow y=16
\end{align}

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