Question

One number is one more than twice another. Their sum is −5. Find the numbers.

Short answer

The numbers are $-2$and $-3$.

Step-by-step solution

Step 1. Given information

We have been given that one number is one more than twice another. Their sum is −5.

We have to find the numbers.

Step 2. Form the equations

From the statement: One number is one more than twice another. Their sum is −5

We get :

$$\begin{gathered} x=2y+1\_\_\_\_\_\_\_\left(1\right) \\ x+y=-5\_\_\_\_\_\_\_\left(2\right) \end{gathered}$$

Step 3. Solve for the equations

Put equation (1) in (2),

$$\begin{gathered} x+y=-5 \\ 2y+1+y=-5 \\ 3y=-6 \\ y=-2 \end{gathered}$$

Put the value of y in (1),

$$\begin{gathered} x=2y+1 \\ x=2(-2)+1 \\ x=-4+1 \\ x=-3 \end{gathered}$$