Question

In the following exercises, translate to a system of equations and solve.

The sum of two numbers is $-26$. One number is 12 less than the other. Find the numbers.

Short answer

The numbers are$-19and-7$

Step-by-step solution

Step 1. Given Information 

The given data is that the sum of two numbers is $-26$. One number is 12 less than the other.

Step 2. Calculation 

Let us assume that x be the first number and y be the second number.

The sum of two number is $-26$implies that $x+y=-26--\left(1\right)$

One number is 12 less than the other implies that$x=y-12--\left(2\right)$

Substitute the value of variable x from equation (2) in equation (1).

$$\begin{gathered} x+y=-26 \\ y-12+y=-26 \\ 2y=-14 \\ y=-7 \end{gathered}$$

Find the value of variable x by using the obtained value of y.

$$\begin{gathered} x=y-12 \\ x=-7-12 \\ x=-19 \end{gathered}$$

Thus, the required ordered pair is$(-19,-7)$