SOLUTION: the sum of 2 numbers is 13. If twice the larger number is increased by 2, the result is equal to 5 times the smaller number. find the numbers. [show all work]

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Question 527770: the sum of 2 numbers is 13. If twice the larger number is increased by 2, the result is equal to 5 times the smaller number. find the numbers. [show all work]
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the larger number and y be the smaller number
Then:
x+y = 13
2x+2 = 5y
We have a system of equations so we can use either the elimination method or substitution method.
Since we have a coefficient of 1 on the first equation, let's use the substitution method.
x+y = 13 ----> y = 13-x
2x+2 = 5y
Substitute 13-x where you see y.
2x + 2 = 5(13-x)
2x + 2 = 65 - 5x
7x = 63
x = 9
Substitute x=9 back into either original equation.
9 + y = 13
y = 4
Thus our two numbers are 9 and 4.