Question

Which two integers have a difference of 24 and a quotient of -7?

Answer 1

So, you have two variables. For simplicity's sake, let's name then x and y.

Condition 1) They have a difference of 24.
\[x - y = 24\]
Condition 2) They have a quotient of -7
\[\frac{ x }{ y } = -7\]
From here, there are multiple algebraic options. But for now, let's just use simple substitution.
\[x = -7y\]
\[(-7y) - y = 24\]
\[-8y = 24\]
\[y = -\frac{ 24 }{ 8 } = ~?\]
How would you further simplify this value? @Miguel980

Answer 2

After you find the y-value, substitute it into either of the two equations above to find your x-value.

By then, you'll have both your unknown integers.