# A first number plus twice a second number is 6. Twice the first number plus the second totals 15 How do you find the numbers?

Nov 17, 2016

The two numbers are: $8$ and $- 1$.

#### Explanation:

If we call the first number $x$ and the second $y$, then we are given:

$\left.\begin{matrix}\text{(i): " x+2y = 6 \\ "(ii): } 2 x + y = 15\end{matrix}\right.$

Multiply both of these equations by $2$ to get:

$\left.\begin{matrix}\text{(iii): " 2x+4y = 12 \\ "(iv): } 4 x + 2 y = 30\end{matrix}\right.$

Then subtracting to eliminate $x$ or $y$:

$\left.\begin{matrix}\text{(iv) - (i): " 3x = 24 color(white)(--) " Hence: " x = 24/3 = 8 \\ "(iii) - (ii): " 3y = -3 color(white)(-) " Hence: } y = \frac{- 3}{3} = - 1\end{matrix}\right.$

So the two numbers are $8$ and $- 1$.