Question

A first number plus twice a second number is 12. Twice the first number plus the second totals 33. Find the numbers.

Answer 1

Answer:

The numbers are -3 and 18 .

Step-by-step explanation:

Let us assume that first number be x.

Let us assume that the second number be y.

As given

A first number plus twice a second number is 12 .

Than the equation becomes

x + 2y = 12

As given

Twice the first number plus the second totals 33.

2x + y = 33

Than the two equations are

x + 2y = 12

2x + y = 33

Multiply x + 2y = 12 by 2 and subtracted from 2x + y = 33

2x - 2x + y - 4y = 33 - 24

-3y = 9

$y = \frac{-9}{3}$

y = - 3

Put in the equation x + 2y = 12

x + 2 ×-3 = 12

x - 6 = 12

x = 12 + 6

x = 18

Therefore the numbers are -3 and 18 .