Chapter 6.3, Problem 2CYP

To determine

To determine the numbers which satisfy the given situation

Answer to Problem 2CYP

The two numbers are 4 and -14.

Explanation of Solution

Given:

The sum of the two numbers is -10.

And, negative 3 times of first number minus the second number is 2.

Calculation:

Let, the two numbers be x and y.

The sum of the two numbers is -10, which means,

  $x+y=-10$

And, negative 3 times of first number minus the second number is 2, which means,

  $-3x-y=2$

Let the equation,

  $x+y=-\mathrm{10.......}(i)$

  $-3x-y=\mathrm{2.......}(ii)$

Now, add equation (i) and equation (ii),

  $\begin{array}{l}\Rightarrow (x+y)+(-3x-y)=-10+2\\ \Rightarrow x+y-3x-y=-8\\ \Rightarrow -2x=-8\\ \Rightarrow x=4\end{array}$

Now, substitute the value of x in equation (i),

  $\begin{array}{l}\Rightarrow 4+y=-10\\ \Rightarrow y=-14\end{array}$

Conclusion:

Therefore, the required numbers are 4 and -14.