Question

The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

Short answer

The numbers are $-3$and $3$.

Step-by-step solution

Step 1. Given information

We have been given that the sum of two numbers is zero. One number is nine less than twice the other.

We have to find the numbers.

Step 2. Form the equations

From the statement: The sum of two numbers is zero. One number is nine less than twice the other.

$$\begin{gathered} x+y=0\_\_\_\_\_\_\_\left(1\right) \\ x=2y-9\_\_\_\_\_\_\_\left(2\right) \end{gathered}$$

Step 3. Solve for the equations

Put equation (2) in (1),

$$\begin{gathered} x+y=0 \\ 2y-9+y=0 \\ 3y-9=0 \\ 3y=9 \\ y=3 \end{gathered}$$

Put the value of y in (2)

$$\begin{gathered} x=2y-9 \\ x=2\left(3\right)-9 \\ x=6-9 \\ x=-3 \end{gathered}$$