Answer:
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')
