SOLUTION: How do I set this up? The larger of two numbers is 1 more than twice the smaller. Three times the larger exceeds 5 times the smaller by 10. Find the numbers.

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Question 238609: How do I set this up? The larger of two numbers is 1 more than twice the smaller. Three times the larger exceeds 5 times the smaller by 10. Find the numbers.
Found 2 solutions by stanbon, JimboP1977:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I set this up? The larger of two numbers is 1 more than twice the smaller. Three times the larger exceeds 5 times the smaller by 10. Find the numbers.
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Let "x" be the larger.
Let "y" be the smaller.
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Equations:
x = 2y+1
2x -5y = 10
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Substitute x = 2y+1 into the 2nd equation and solve for "y":
2(2y+1) - 5y = 10
-y = 8
y = -8
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Substitute y =-8 into x = 2y+1 to solve for "x":
x = 2*-8+1 = -15
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Cheers,
Stan H.

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
x = larger number
y = smaller number
x=2y+1 (1)
3x-10=5y (2)
(1) multiply by 3 gives:
3x=6y+3 (3)
Rearrange (2) 3x=5y+10
(3)-(2)
0=y-7
y=7
x=15