1 Answer

Tohuwawohu · Answer 1 · 2023-10-06T09:33:45+0000

Let x and y be the unknown numbers.

We know that one number is 10 more than the other, this can be express as:

We also know that twice the sum of both numbers is equal to 8, the sum of the two numbers is:

Twice this sum is:

And this have to be equal to 8, then we have the equation:

Hence we have the system of equations:

$\begin{gathered} y=x+10 \\ 2x+2y=8 \end{gathered}$

To solve this system we take the expression for y from the first equation and plug it in the second, then we solve for x:

$\begin{gathered} 2x+2(x+10)=8 \\ 2x+2x+20=8 \\ 4x+20=8 \\ 4x=8-20 \\ 4x=-12 \\ x=-(12)/(4) \\ x=-3 \end{gathered}$

Now that we know the value of x we plug it in the expression for y:

$\begin{gathered} y=-3+10 \\ y=7 \end{gathered}$

Therefore the numbers we are looking for are -3 and 7

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