MHB Solve for the Two Numbers: Sum 9, Difference 6

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SUMMARY

The problem involves finding two numbers where their sum is 9 and their difference is 6. By defining the smaller number as \( x \) and the larger number as \( x + 6 \), we can set up the equations \( x + (x + 6) = 9 \) and \( x - (x + 6) = 6 \). Solving these equations leads to the conclusion that the two numbers are 3 and 6.

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paulmdrdo1
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can you help me solve this just using one variable

the sum of two numbers is 9 and their difference is 6. what are the numbers?

thanks!
 
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paulmdrdo said:
the sum of two numbers is 9 and their difference is 6. what are the numbers?
Let $x$ be the smaller of the two numbers. Since the difference is 6, the other number is $x+6$. Now try writing the equation saying that the sum of these numbers is 9 and try solving it.
 
Alternatively:

$x + y = 9$
$x - y = 6$

The second equation tells us:

$x = y + 6$

So substitute that value for $x$ into the first equation, to get an equation in the single variable $y$.
 

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