Question

Use a system of linear equations with two variables and two equations to solve.A number is 13 more than another number. Twice the sum of the two numbers is 6. Find the two numbers. (Enter your answers as a comma-separated list.)

Answer 1

Given

A number is 13 more than another number. Twice the sum of the two numbers is 6.

To find the two numbers.

Explanation:

It is given that,

A number is 13 more than another number.

And, Twice the sum of the two numbers is 6.

Let x and y be the two numbers.

Then,

$\begin{gathered} x=y+13\text{ \_\_\_\_\_\_\_\lparen1\rparen} \\ 2(x+y)=6\text{ \_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}$

That implies,

$\begin{gathered} 2(y+13+y)=6 \\ 2y+13=\frac{6}{2} \\ 2y+13=3 \\ 2y=3-13 \\ 2y=-10 \\ y=-\frac{10}{2} \\ y=-5 \end{gathered}$

Also,

$\begin{gathered} x=-5+13 \\ x=8 \end{gathered}$

Hence, the two numbers are 8, -5.