Question

K

A first number plus twice a second number is 10. Twice the first number plus the second
totals 23. Find the numbers.
The smaller of the two numbers is
The larger of the two numbers is
...

Answer 1

First number is 12

Second number is -1

The smaller of the two numbers is the second number.

The larger of the two numbers is the first number.

Explanation:

let a = first number and b = second number

a + 2b = 10 eq.1

2a + b = 23 eq.2

multiply equation 2 by -2 to eliminate b

-2(2a + b = 23)

-4a - 2b = -46 eq.3

add equations 1 and 3

a + 2b = 10

-4a - 2b = -46

____________

-3a = -36

a = 12

substitute a = 12 to any of the equations

I use equation 1

a + 2b = 10

12 + 2b = 10

2b = -12

b = -1