Answer:
The two integers have values 28 and 21
Step-by-step explanation:
This is a simultaneous equation problem. Let the two integers be represented by [tex]a[/tex] and [tex]b[/tex].
The first part of the question can be represented by the following equation:
[tex]a-b=7[/tex]
From the second part of the question, we know their sum is 49, which can be represented by:
[tex]a+b=49[/tex]
Now, we need to manipulate the expressions to contain just one unknown value. If we add [tex]b[/tex] to both sides of the first equation we get:
[tex]a=b+7[/tex]
Now we can substitute the value of [tex]a[/tex] for [tex]b+7[/tex] in the second equation:
[tex]a+b=(b+7)+b=49[/tex]
Which we can then rearrange and solve for [tex]b[/tex]:
[tex]2b +7=49\\2b=42\\b=21[/tex]
We can now use the value for [tex]b[/tex] in either of the two original equations for find the value of [tex]a[/tex]:
[tex]a=b+7=(21)+7=28[/tex].
We now have the the two values 28 and 21.
Note: To double check the answer, check if their sum is equal to 49:
[tex]a+b=28+21=49[/tex].
