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:
[tex]x+2y=8...(1)[/tex]
We are also given that twice the first number plus the second totals 31. We can represent this information as:
[tex]2x+y=31...(2)[/tex]
Now let us solve our system of equations using substitution method.
From equation (1) we will get,
[tex]x=8-2y[/tex]
Substituting [tex]x=8-2y[/tex] in equation (2) we will get,
[tex]2(8-2y)+y=31[/tex]
[tex]16-4y+y=31[/tex]
[tex]-4y+y=31-16[/tex]
[tex]-3y=15[/tex]
[tex]y=\frac{15}{-3}[/tex]
[tex]y=-5[/tex]
Therefore, the second number is -5.
Now let us substitute y=-5 in equation (1).
[tex]x+(2*-5)=8[/tex]
[tex]x-10=8[/tex]
[tex]x=8+10[/tex]
[tex]x=18[/tex]
Therefore, the first number is 18.
