SOLUTION: The difference of twice one number and five time another number is 11. The first number is three time the second number increased by 6. What are the numbers?

Question 1008455: The difference of twice one number and five time another number is 11. The first number is three time the second number increased by 6. What are the numbers?
Found 2 solutions by macston, fractalier:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
F=first number; S=second number
.
F=3S-6
.
2F-5S=11
2(3S-6)-5S=11
6S-12-5S=11
S=23
.
ANSWER 1: The second number is 23.
.
F=3S-6=3(23)-6=69-6=63
ANSWER 2: The first number is 63.
.
CHECK:
2F-5S=11
2(63)-5(23)=11
126-115=11
11=11

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the first and second numbers, x and y. Then we write
2x - 5y = 11 and
x = 3y + 6
Now substitute the second equation into the first and get
2(3y+6) - 5y = 11
6y + 12 - 5y = 11
y + 12 = 11
y = -1 and
x = 3(-1) + 6 = 3
Your numbers are 3 and -1.
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