A first number plus twice a second number is 10. Twice the first number plus the second totals 32. Find the numbers.

Let first number be x

And the second number be y

Then, x + 2y = 10.

⇒ x = 10 - 2y ... (1)

Also, 2x + y = 32 ... (2)

From, equation (1) & (2) we get,

2 (10-2y) + y = 32

or 20 - 4y + y = 32

or 20 - 32 = 3y

or y = 4

Therefore, x = 10 - 2y

or x = 10-2*4

or x = 10 - 8

or x = 2

Therefore, the two numbers are 2 & 4

First num = x, second num=y

X+2y=10

2x+y=32

Use equation 1 in equation 2

X=10-2y

2 (10-2y) + y=32

20-4y+y=32

-3y = 12

Y = - 4

X+2 (-4) = 10

X=10+8

X=18

Firstnum = 18, second num = - 4