Question

Solve the following word problem using elimination. Set up a system of equations before solving.

Answer 1

Let x and y be the two numbers. x will be the larger number and y the smaller one.

According to the given information, the difference of x and y is 4:

`x-y=4`

The sum of y and 3 times x is 36:

`3x+y=36`

So the system of equations is:

`\begin{gathered} x-y=4 \\ 3x+y=36 \end{gathered}`

Solve the system by elimination by adding these equations:

x has a value of 10. Use this value and the first equation to find y:

`\begin{gathered} x-y=4 \\ y=x-4 \\ y=10-4 \\ y=6 \end{gathered}`

y has a value of 6.

It means that the 2 numbers are 10 and 6.