A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

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A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.

Givens and assumptions:

• Let the first number be x.
• Let the second number be y.
• Twice means multiply by 2
• The phrases is and totals mean equal to

We're given two equations:

1. x + 2y = 14
2. 2x + y = 40

To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:

1. -2x - 4y = -28
2. 2x + y = 40

Now add both equations together
(-2 _ 2)x (-4 + 1)y = -28 + 40
-3y = 12

To solve this equation, we type it in our search engine and we get:
y = -4

We substitute this back into equation 1 for y = -4:
x + 2(-4) = 14
x - 8 = 14

To solve this equation for x, we type it in our search engine and we get:
x = 22