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.

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) (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,

and if,

then,

therefore, since we now know what y equals, plug it back into the equation,

now plug that x value into the equation,
so that you have

NOW you can also solve this by using a system of equations.
the first equation is and the second is
place one on top of the other

now notice if you multiply by positive 5 and add the two equations, you will be able to eliminate the x.
+ =
therefore, and now once again plug y in and solve for x and you get 7.
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