Question

first number plus twice a second number is 8. Twice the first number plus the second totals 31. Find the number

Answer 1

1st number = 18

2nd number = -5

Explanation:

Let x be first number and y be the 2nd number.

We have been given that first number plus twice a second number is 8. We can represent this information as:

`x+2y=8...(1)`

We are also given that twice the first number plus the second totals 31. We can represent this information as:

`2x+y=31...(2)`

Now let us solve our system of equations using substitution method.

From equation (1) we will get,

`x=8-2y`

Substituting
`x=8-2y` in equation (2) we will get,

`2(8-2y)+y=31`

`16-4y+y=31`

`-4y+y=31-16`

`-3y=15`

`y=(15)/(-3)`

`y=-5`

Therefore, the second number is -5.

Now let us substitute y=-5 in equation (1).

`x+(2*-5)=8`

`x-10=8`

`x=8+10`

`x=18`

Therefore, the first number is 18.