Question

The sum of two numbers is 80 If four times the smaller number is subtracted from the larger number, the result is 10. Find the two numbers. The larger number is? The smaller number is?

Answer 1

Let x be the smallest number & y the largest:

x + y  = 80
y - 4x = 10
Solving this equation gives :
x =14 & y = 66

Answer 2

This can be solved using a system of equations. 
$\left \{ {{x+y=80} \atop {x-4y=10} \right.$
Subtract y from both sides.
$x=80-y$
Substitute:
$80-y-4y=80-5y=10$
Subtract 80 from both sides:
$5y=70$
Divide both sides by 5:
$y= \frac{70}{5} =14$
Substitute.
$x=80-14=66$