Question

The sum of two numbers is

$-45$. Their difference is $-89$.

Find the numbers.

Short answer

The numbers are$-67\&22$.

Step-by-step solution

Step 1. Given

Sum$=-45$and the difference is$-89$.

Step 2. Calculation

Let the numbers are$x\&y$

Therefore,$x+y=-45$

and the difference is$x-y=-89$

Add the two equations,

$$\begin{gathered} x+y=-45\&x-y=-89 \\ x+y+x-y=-45+(-89) \\ 2x=-134 \\ x=-67 \end{gathered}$$

Now put value of$x$in any equation and find the value of $y$.

$$\begin{gathered} x+y=-45 \\ -67+y=-45 \\ y=-45+67 \\ y=22 \end{gathered}$$

Therefore the numbers are$-67\&22$

Step 3. Verification

Verify the equation,

$$\begin{gathered} x+y=-45 \\ -67+22=-45 \\ -45=-45 \end{gathered}$$

LHS is equal to RHS