Question

Three times a number minus another number is $-3$.

The sum of the numbers is $11$.

What are the numbers?

Answer 1

To find the numbers:

Let $x$ be the first number and $y$ be the second number.

Three times a number minus another number is $-3$.

$3x-y=-3...\left(1\right)$

The sum of the numbers is $11$.

$x+y=11...\left(2\right)$

On adding both equations $\left(1\right)$ and $\left(2\right)$:

$\begin{array}{rcl}3x-y+x+y& =& -3+11\\ & \Rightarrow & 4x=8\\ & \Rightarrow & x=\frac{8}{4}\left[\text{Divide by}4\right]\\ \therefore x& =& 2\end{array}$

Now, substitute the value of $x$ in the equation $\left(2\right)$:

$\begin{array}{rcl}2+y& =& 11\\ & \Rightarrow & y=11-2\left[\text{Subtract 2 both sides}\right]\\ \therefore y& =& 9\end{array}$

Therefore, $x$ is $2$ and $y$ is $9$.

Hence, the numbers are $\mathbf{2}$ and $\mathbf{9}$.