Question

One number is two more than four times another. Their sum is$-13$. Find the numbers.

Short answer

If one number is two more than four times another and their sum is $-13$then those numbers are$-3\&-10$.

Step-by-step solution

Step 1. Given information  

The second number is $2$more than $4$times the first number.

The sum of the first number and the second number is $-13$.

Step 2. Consider variable for numbers 

Consider the first number is n.

The second number is $2$more than $4$times the first number.

So the second number is$4n+2$.

Step 3. Solution  

The sum of the first number and the second number is$-13$.

$$\begin{gathered} n+(4n+2)=-13 \\ 5n+2=-13 \\ 5n=-15 \\ n=-3 \end{gathered}$$

The first number is $-3$.

The second number is:

$$\begin{gathered} 4n+2=4(-3)+2 \\ =-12+2 \\ =-10 \end{gathered}$$

So the numbers are$-3\&-10$.

Step 4. Verification 

$-10$is $2$more than $4$times of role="math" $-3$

$$\begin{gathered} -10\stackrel{?}{=}4(-3)+2 \\ -10\stackrel{?}{=}-12+2 \\ -10=-10 \end{gathered}$$

The left-hand side is equal to the right-hand side

The sum of $-3\&-10$is $-13$

$$\begin{gathered} (-3)+(-10)\stackrel{?}{=}-13 \\ -3-10\stackrel{?}{=}-13 \\ -13=-13 \end{gathered}$$

The left-hand side is equal to the right-hand side, so our answer is correct

the numbers are$-3\&-10$