Chapter 6.3, Problem 22PPS

To determine

To find the numbers

Answer to Problem 22PPS

4, 0

Explanation of Solution

Given:

A number minus twice another number is 4.

Three times the first number plus two times the second number is 12.

Calculation:

Let the first number be x and the second number be y .

Given that, a number minus twice another number is 4.

So, $x-2y=4\to (1)$

Also, three times the first number plus two times the second number is 12. Then,

  $3x+2y=12\to (2)$

Solving above two equations using elimination method,

Add equations (1) and (2), so that the variable y can be eliminated.

  $\begin{array}{l}x-2y=4\\ \frac{3x+2y=12}{4x=16}\end{array}$

  $\begin{array}{c}4x=16\text{ [Dividing 4 on both sides]}\\ x=\frac{16}{4}\\ x=4\end{array}$

Substitute the value of $x=4$ in any one of the equations.

Say, equation (1),

  $\begin{array}{c}4-2y=4\text{ [Subtracting 4 on both sides] }\\ -2y=4-4\\ -2y=0\\ y=0\end{array}$

Conclusion:

Therefore, the numbers are 4 and 0.