Question

The sum of two numbers is

$-27$. Their difference is $-59$.

Find the numbers.

Short answer

The numbers are$-43\&16$.

Step-by-step solution

Step 1. Given

Sum$=-27$and the difference is$-59$

Step 2. Calculation

Let the numbers are$x\&y$

Therefore,$x+y=-27$

and the difference is$x-y=-59$

Add the two equations,

$$\begin{gathered} x+y=-27\&x-y=-59 \\ x+y+x-y=-27+(-59) \\ 2x=-86 \\ x=-43 \end{gathered}$$

Now put value of in any equation and find the value of .

$$\begin{gathered} x+y=-27 \\ -43+y=-27 \\ y=-27+43 \\ y=16 \end{gathered}$$

Therefore the numbers are$-43\&16$

Step 3. Verification

Verify the equation,

$$\begin{gathered} x+y=-27 \\ -43+16=-27 \\ -27=-27 \end{gathered}$$

LHS is equal to RHS.