Answer
Let's represent the unknown number with x and y
Step 1
Their sum
[tex]x+y\text{ =86}[/tex]
Step 2
Their difference
[tex]x-y=18[/tex]
Step 3
We are asked to solve the simultaneous equation by elimination method
[tex]\begin{gathered} x+y=86_{} \\ x-y=18 \\ \text{add the equation} \\ 2x=104 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{104}{2} \\ \\ x=52 \end{gathered}[/tex]
Step 4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
[tex]x+y=86[/tex]
we substitute 52 for x in x+y=86
[tex]\begin{gathered} 52+y=86 \\ \text{collect the like terms} \\ y=86-52 \\ y=34 \end{gathered}[/tex]
The final answer
Smaller of the two number = 34
