Question

the sum of two numbers is 86 their difference is 18 write a system of equations that describe the situation solved by elimination to find the two numbers

Answer 1

Let's represent the unknown number with x and y

Step 1

Their sum

`x+y\text{ =86}`

Step 2

Their difference

`x-y=18`

Step 3

We are asked to solve the simultaneous equation by elimination method

`\begin{gathered} x+y=86_{} \\ x-y=18 \\ \text{add the equation} \\ 2x=104 \\ \text{divide both sides by 2} \\ (2x)/(2)=(104)/(2) \\ \\ x=52 \end{gathered}`

Step 4

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

`x+y=86`

we substitute 52 for x in x+y=86

`\begin{gathered} 52+y=86 \\ \text{collect the like terms} \\ y=86-52 \\ y=34 \end{gathered}`

The final answer

Smaller of the two number = 34