Question

Three times a first number increased by a second number is 21. The first number decreased by twicethe second number is -14. Find the numbers.

Answer 1

`\text{Let x the first number and y, the second number}`

Mathematical representation of statement 1 is:

`3x+y=21`

Mathematical representation of statement 2 is:

`x-2y=-14`

Solving the two(2) equations simultaneously by the method of elimination, we have:

`\begin{gathered} 3x+y=21\text{ -------}*2 \\ x-2y=-14 \\ ----------------------- \\ 6x+2y=42 \\ x-2y=-14 \\ ----------------------- \\ 6x+x=42-14 \\ 7x=28 \\ x=(28)/(7) \\ x=4 \end{gathered}`

Substitute for x = 4 into any of the two(2) equations:

`\begin{gathered} \text{from eqn i}i) \\ x-2y=-14 \\ 4-2y=-14 \\ -2y=-14-4 \\ -2y=-18 \\ y=-(18)/(-2) \\ y=9 \end{gathered}`

Hence, the numbers are 4 and 9