Simple math
Let x be the smaller integer and y the larger integer
So the first equation will be like this
y - x = 9
and the second will be
5x = 9 + 3y
Let's compute for y using the first equation
y - x = 9
move y to the right and change sign
y = x + 9
Let''s now use x here to replace x in the second equation
5x = 9 + 3(x + 9)
Multiply
5x = 9 + 3x + 27
Add
5x = 3x + 36
Move 3x to the left and change sign
5x - 3x = 36
Subtract
2x = 36
Divide by 2 to eliminate the 2 in the 2x
2x/2 = 36/2
x = 18
Let us now use the value of y to know the real value of x in the first equation.
y = x + 9
y = 18 + 9
y = 27
Let's check
y - x = 9
27 - 18 = 9
9 = 9 correct
Let's use the second equation
5x = 9 + 3y
5(18) = 9 + 3(27)
90 = 9 + 81
90 = 90 correct
I hope it helps
