Q 78 - Intermediate Algebra

Question

The sum of two numbers is

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

Find the numbers.

Step-by-Step Solution

Answer

The numbers are $-43 \& 16$.

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.