Question 4: Find two numbers whose sum is \(68\) and difference is \(22\).
Solution:
Let \(x\) and \(y\) are two required numbers
According to the given condition of question
\[
\begin{align*}
x+y&=68\_\_\_\_( 1)\\
x-y&=22\_\_\_\_( 2)\\
\end{align*}
\]
Adding both equations, we have
\[
\begin{align*}
x+y+x-y&=68+22\\
2x&=90\\
x&=\frac{90}{2}\\
x&=45\\
\end{align*}
\]
Put \(x=45\) in equation \((1)\)
\[
\begin{align*}
45+y&=68\\
y&=68-45\\
y&=23\\
\end{align*}
\]