A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers.

Let the first number be x. Let the second number be y. We're given two equations:

1. x + 2y = 6
2. 2x + y = 15

Multiply the first equation by -2:

1. -2x - 4y = -12
2. 2x + y = 15

Now add them
-2x + 2x - 4y + y = -12 + 15
-3y = 3

Divide each side by -3:
y = 3/-3
y = -1

Plug this back into equation 1:
x + 2(-1) = 6
x - 2 = 6

To solve for x, we type this equation into our search engine and we get:
x = 8