Answer: The 2 (TWO) numbers are: 18 and 24 .
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Explanation:
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x + y = 42 ; Let "x" be the 'smaller number' ; "y'' be the "larger number";
so: x = y − 6 ;
Now, substitute "y−6" for "x" in the equation:
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x + y = 42 ;
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y − 6 + y = 42
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Combine the "like terms", which appear on the left-hand side of the equation:
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y + y , = 2y ; and rewrite the equation:
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2y − 6 = 42 ;
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Now, add "6" to each side of the equation:
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2y − 6 + 6 = 42 + 6 ;
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to get: 2y = 48 ;
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Now, divide EACH side of the equation by "2"; to isolation "y" on one side of the equation; and to solve for "y" ;
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2y / 2 = 48 / 2 ;
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to get: y = 24 ; which is the value of one of the number we which to solve for —specifically, the larger number.
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Now, we can use one of two methods to solve for "x". In fact, let us use BOTH methods, to ensure we have the same value for "x" (which serves a purpose for confirming our answer and checking our work). We can start with EITHER method, first in EITHER ORDER; nonetheless, I shall still list them as "Method 1" and "Method 2"—as follows:
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Method 1)
From the original problem, "The smaller number is 6 less than the smaller number" ; or: " x = y − 6 " .
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Since our obtained/ solved value for "y" is "24" ; we can plug in the value, "24", for "y"; into this equation; and solve for "x" ;
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x = y − 6 = 24 - 6 ;
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to get: x = 18 . which is the other value we wish to obtain, the "smaller number" value.
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Method 2)
From the original problem: "The sum of two numbers is 42. ...." ;
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or, " x + y = 42 " .
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Using our obtained/solved value for "y", which is: "24", we can plug this value, "24", for "y", into the above equation; and solve for "x";
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x + y = 42 ;
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x + 24 = 42 ;
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Now, subtract "24" from EACH side of the equation, to isolate "x" on one side of the equation; and to solve for "x" ;
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x + 24 − 24 = 42 − 24 ;
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x = 18 ; which is the same value we got for "x" from: "Method 1" above.
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So, the two numbers are: "18" and "24". Do they add up to "42"?
18 + 24 =? 42?? Yes.
Is the "smaller number" (18) , "6 less than the larger number (24)?
Does 18 + 6 =? 24 ?? Yes! Does 24 − 6 =? 18 ?? Yes!
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So the two (2) numbers are: 18 and 24 .
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