Answer:
[tex]\large \boxed{x = 14; y = -24}[/tex]
Step-by-step explanation:
1. Translate
x and y = two integers
x + y = the sum of two integers
x - y = the difference between two integers Then,
x + y = -10 and
x - y = 38
2. Solve
[tex]\begin{array}{rcrl}(1) \qquad x + y & = & -10&\\(2) \qquad x - y & = &38&\\(3) \qquad \quad 2x & = &28&\text{Added (1) and (2)}\\(4) \qquad \qquad x & = & \mathbf{14}&\text{Divided (3) by 2}\\ 14 + y & = & -10&\text{Subtituted (4) into (1)}\\y & = &\mathbf{-24}& \text{Subtracted 14 from each side}\\\end{array}\\\text{The integers are $\large \boxed{\mathbf{x = 14; y = -24}}$}[/tex]
3. Check:
[tex]\begin{array}{ccc}14 + (-24) = -10 & \qquad & 14 - (-24) = 38\\14 - 24 = -10 & \qquad & 14 + 24 = 38\\-10 = -10 & \qquad & 38 = 38\\\end{array}[/tex]
OK
