As given by the question
There are given that the sum of the two numbers is at least 8.
Now,
Let the unknown numbers be x and y
Then,
If the sum of the two numbers is at least 8 then:
[tex]x+y\ge8[/tex]
Similarly, the sum of one of the numbers and 3 times the second number is no more than 15
Then,
[tex]x+3y\leq15[/tex]
Now,
From the both of the inequality:
[tex]\begin{gathered} x+y\ge8 \\ x+3y\leq15 \end{gathered}[/tex]
Then, find the first and second nuber:
So,
[tex]\begin{gathered} x+y\ge8 \\ x\ge8-y\ldots(a) \end{gathered}[/tex]
Then, Put the value of x into the second equation
Then,
[tex]\begin{gathered} x+3y\leq15 \\ 8-y+3y\leq15 \\ 8+2y\leq15 \\ 2y\leq15-8 \\ y\leq\frac{7}{2} \\ y\leq3.5 \end{gathered}[/tex]
Then,
Put the value of y into the equation (a)
[tex]\begin{gathered} x\ge8-y \\ x\ge8-3.5 \\ x\ge4.5 \end{gathered}[/tex]
Hence, the first number and second number is shown in below:
[tex]\begin{gathered} x\ge4.5 \\ y\leq3.5 \end{gathered}[/tex]
The graph of the given result is shown below:
