SOLUTION: Could you show me the steps you take to solve: The sum of two integers is thirty. Eight times the smaller integer is six more than five times the larger integer. Find the integers

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Question 155294: Could you show me the steps you take to solve:
The sum of two integers is thirty. Eight times the smaller integer is six more than five times the larger integer. Find the integers.
Found 2 solutions by stanbon, nerdybill:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of two integers is thirty.
x + y = 30
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Eight times the smaller integer is six more than five times the larger integer.
8x = 5y +6
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Arrange for elimination:
8x + 8y = 240
8x - 5y = 6
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Find the integers.
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Subtract the 2nd equation from the 1st to get:
13y = 234
y = 18 (larger integer)
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Substitute into x + y = 30 to solve for "x":
x + 18 = 30
x = 12 (smaller integer)
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Cheers,
Stan H.

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The sum of two integers is thirty. Eight times the smaller integer is six more than five times the larger integer. Find the integers.
.
Assign variables to things you don't know.
Let x = larger integer
and y = smaller integer
.
Since we have two unknowns, we'll need to find two equations.
From: "The sum of two integers is thirty." we get equation 1:
x+y = 30
.
From: "Eight times the smaller integer is six more than five times the larger integer." we equation 2:
8y = 5x+6
.
To solve, let's solve equation 1 for 'x':
x+y = 30
x = 30-y
.
Substitute the above into equation 2 and solve for y:
8y = 5x+6
8y = 5(30-y)+6
8y = 150-5y+6
13y = 150+6
13y = 156
y = 156/13
y = 12 (value of smaller integer)
.
Substitute the above into equation 1 and solve for x:
x+y = 30
x+12 = 30
x = 30-12
x = 18 (value of larger integer)