Q 79 - Intermediate Algebra

Question

The sum of two numbers is

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

Find the numbers.

Step-by-Step Solution

Answer

The numbers are $-67 \& 22$.

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