The sum of two numbers is twenty-five Twelve less than four times one of the numbers is sixteen more than twice the other number?

Let's label one of the numbers with x, and the other number with y. So,

x + y = 25

4x - 12 = 2y + 16 add 12 and subtract 2y to both sides of the second equation; x + y = 25

4x - 2y = 16 +12 multiply by -4 the first equation; -4x - 4y = -100

4x - 2y = 16 +12 add both equations in order to eleminate x; 0 - 6y = -72 multiply by -1 to both sides;

6y = 72 divide by 6 both sides;

y = 12 Substitute 12 for y into the first equation;

x + y = 25

x + 12 = 25 subtract 12 to both sides;

x = 13

Thus, the numbers are 13 and 12. Check:

13 + 12 = 25

4(13) -12 = 2(12) +16 ?

52 -12 = 24 + 16 ?

40 = 40