Question 242805
In the setup to the problem, always try to minimize the unknowns.
x = one number
It is 11 more than twice another number.
y = another number
x = 2y + 11
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Now the second part says if the sum of x + y is decreased by 9 (that is:  x + y - 9), the result is 17.
x + y - 9 = 17
Add 9 to both sides
x + y = 17+9 = 26
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Now we have to solve x and y
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Subtracting y from both sides of the equation above.
x + y - y = 26 - y
x = 26 - y
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Substituting in the other equation.
x = 2y + 11
26 - y = 2y + 11
Adding y to both sides
26 = 3y + 11
Subtracting 11 from both sides
15 = 3y
Dividing both sides by 3
5 = y
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y = 5
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Recall
x + y = 26
Substituting for y
x + 5 = 26
Subtracting 5 from both sides
x = 21
Check your work (even if you're tired)...
Does x = 2y + 11?
21 = 2(5) + 11?
Yes it does.
Does x + y - 9 = 17?
21 + 5 - 9 = 17?
Yes it does.
So we're done.
x = 21
y = 5