Question

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

Answer 1

Answer:

1st number = 18

2nd number = -5

Step-by-step 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,

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

$16-4y+y=31$

$-4y+y=31-16$  

$-3y=15$  

$y=\frac{15}{-3}$

$y=-5$

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.