SOLUTION: three times a number increades 5 times another number is 49 but twice the second number exceeds 5 times the first number by 1.what are the numbers?

Question 135783: three times a number increades 5 times another number is 49 but twice the second number exceeds 5 times the first number by 1.what are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = "a number"
Let y = "another number"
:
Write an equation for each statement:
:
"three times a number increased 5 times another number is 49"
3x + 5y = 49
:
"twice the second number exceeds 5 times the first number by 1."
2y = 5x + 1
In standard form
-5x + 2y = 1
:
what are the numbers?
:
Multiply the 1st equation by 5, and the 2nd equation by 3
15x + 25y = 245
-15x + 6y = 3
-----------------Adding eliminates, x; find y:
0x + 31y = 248
:
y =
y = 8
:
Find x using the 1st equation
3x + 5(8) = 49
3x = 49 - 40
x =
x = 3
:
Check solutions in the 2nd equation:
2(8) = 5(3) + 1
16 = 15 + 1; confirms our solution
:
:
Did this make sense to you? Any questions?

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