SOLUTION: Five times a number plus four times a second number equal to eighty-three. The difference between the two numbers is 5. Find the two numbers.

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Question 622413: Five times a number plus four times a second number equal to eighty-three. The difference between the two numbers is 5. Find the two numbers.
Answer by matineesuxxx(27) About Me  (Show Source):
You can put this solution on YOUR website!
let x represent the smaller number,
let y represent the larger number
therefore,
"five times a number plus four times a second number is 83"
that means,
5x%2B4y=83
and if,
y-x=5
then,
y=5%2Bx
therefore, since we now know what y equals, plug it back into the equation,
5x%2B4%285%2Bx%29=83
5x%2B20%2B4x=83
9x%2B20=83
9x=63
x=63%2F9
x=7
now plug that x value into the equation,
y-x=5 so that you have
y-7=5
y=12
NOW you can also solve this by using a system of equations.
the first equation is 4y%2B5x=83 and the second is y-x=5
place one on top of the other
4y%2B5x=83
y-x=5
now notice if you multiply y-x=5 by positive 5 and add the two equations, you will be able to eliminate the x.
4y%2B5x=83 + 5y-5x=25 = 9y=108
therefore, y=12 and now once again plug y in and solve for x and you get 7.