Chapter 6.3, Problem 21PPS

To determine

To find the numbers

Answer to Problem 21PPS

9, 2

Explanation of Solution

Given:

Three times of a number minus another number is -3

Sum of the numbers: 11

Calculation:

Let x and y be the two numbers.

Given that, three times of a number minus another number is -3.

So, $3x-y=-3\to (1)$

Also, sum of the numbers is 11.Then,

  $x+y=11\to (2)$

Solving the above two equations using elimination method,

Multiply (2) by 3, so that the variable x can be eliminated.

  $3x+3y=33\to (3)$

Subtract (1) from (3)

  $\begin{array}{l}\text{ 3}x+3y=33\\ \frac{-3x+y=3}{4y=36}\text{ [When subtracting the sign of (1) changes]}\end{array}$

  $\begin{array}{c}4y=36\text{[Dividing 4 on both sides]}\\ y=\frac{36}{4}\\ y=9\end{array}$

Substitute the value of $y=9$ in any one of the equations.

Say, equation (2),

  $\begin{array}{c}x+9=11\text{ [Subtracting 9 on both sides] }\\ x=11-9\\ x=2\end{array}$

Conclusion:

Therefore, the numbers are 9 and 2.