A first number plus twice a second number is 11. Twice the first number plus the second totals 16. Find the numbers.

The first number, x, is equal to 7. The second number, y, is equal to 2.

x + 2y = 11

2x + y = 16

We can subtract 2y from both sides of the first equation to get a value for x.

x = 11 - 2y

Because we have a value for x, we can plug it into the second equation.

2 (11 - 2y) + y = 16

Distributive property.

22 - 4y + y = 16

Combine like terms.

22 - 3y = 16

Subtract 22 from both sides.

-3y = - 6

Divide both sides by - 3.

y = 2

Now that we have a value for y, we can plug it into either equation to solve for x.

x + 2 (2) = 11

x + 4 = 11

Subtract 4 from both sides.

x = 7