Question

The sum of two number is

$-26$. One number is $12$less than

the other. Find the numbers.

Short answer

The numbers are$-7$and$-19$

Step-by-step solution

Step 1. Given information

Sum $=-26$and one number is $12$less than other.

Step 2. Calculation

Let the numbers are $x\&y$

Then $x+y=-26$and role="math" localid="1644381520247" $y=12-x$

Now, find the value of y and put in the first equation and simplify them.

role="math" localid="1644381539282" $$\begin{gathered} y=12-x \\ x-y=-26 \\ x-(12-x)=-26 \\ x+x-12=-26 \\ 2x=-26+12 \\ 2x=-14 \\ x=-7 \end{gathered}$$

Now, put value of $x$in any equation and solve for the value of $y$

$$\begin{gathered} x+y=-26 \\ -7+y=-26 \\ y=-26+7 \\ y=-19 \end{gathered}$$

Therefore the numbers are$-7\&-19$

Step 3. Verification

Put values in the equation to verify,

$$\begin{gathered} x+y=-26 \\ -7+(-19)=-26 \\ -7-19=-26 \\ -26=-26 \end{gathered}$$

LHS is equal to RHS.