The sum of two numbers is 18. twice the first number increased by three times the second number equals 40. find the numbers

4 and 14

Step-by-step explanation:

:the sum of two numbers is 18" can be written as

 x + y = 18               let x represent the first number, and y the second

"twice the first number increased by three times the second number equals 40" can be written as

2x + 3y = 40

Now solve this system. Using elimination will probably be the easier method...

1.   x +  y = 18

2.  2x + 3y = 40

Multiply equation 1 by -2 so the x variable will be the opposite of the x variable on equation 2.

1.  -2x - 2y = -36

2.  2x  + 3y = 40

Now add the equations together, cancelling out 'x'

y  = 4     ( 2x + (-2x) = 0, so 'x' is gone, 3y + (-2y) = y, 40 + (-36) = 4)

Since y = 4, plug that into either equation 1 or 2 and solve for x

1.  x + 4 = 18     (y becomes 4)

     x = 14        (subtract 4 on both sides to isolate 'x')