Answer :
Answer: The two numbers are 9 and 6
We can deduce from the question that we need 2 numbers. Lets start by defining the two numbers.
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Define the two numbers
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Let one number be x and the other number be y.
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Construct the first equation (Sum)
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The sum of the two numbers is 15.
x + y = 15
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Construct the second equation (Difference)
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The difference of the numbers is 3
x - y = 3
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Use the two equations to solve x and y
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x + y = 15 -------------------- (equation 1)
x - y = 3 -------------------- (equation 2)
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Make x the subject in equation 2
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x - y = 3 ← Add y to both sides
+ y +y
x = 3 + y
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Substitute x = 3 + y into equation 1
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x + y = 15 ←Substitute x = (3+y)
(3 + y) + y = 15
3 + y + y = 15 ←Combine like terms
2y + 3 = 15 ←take away 3 from both sides
-3 -3
2y = 12 ←Divide by 2 on both side to get 1 y
÷2 ÷2
y = 6
Now we know y =6, substitute it into equation 1 to find x
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Substitute y = 6 into equation 1 to find x
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x + y = 15 ←Substitute y = 6
x + 6 = 15 ←take away 6 from both sides
-6 -6
x = 9
Now we know x = 9
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Find the two numbers
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first number = x = 9
second number = y = 6
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Answer: The two numbers are 9 and 6
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We can deduce from the question that we need 2 numbers. Lets start by defining the two numbers.
---------------------------------------------------------------
Define the two numbers
---------------------------------------------------------------
Let one number be x and the other number be y.
---------------------------------------------------------------
Construct the first equation (Sum)
---------------------------------------------------------------
The sum of the two numbers is 15.
x + y = 15
---------------------------------------------------------------
Construct the second equation (Difference)
---------------------------------------------------------------
The difference of the numbers is 3
x - y = 3
---------------------------------------------------------------
Use the two equations to solve x and y
---------------------------------------------------------------
x + y = 15 -------------------- (equation 1)
x - y = 3 -------------------- (equation 2)
---------------------------------------------------------------
Make x the subject in equation 2
---------------------------------------------------------------
x - y = 3 ← Add y to both sides
+ y +y
x = 3 + y
---------------------------------------------------------------
Substitute x = 3 + y into equation 1
---------------------------------------------------------------
x + y = 15 ←Substitute x = (3+y)
(3 + y) + y = 15
3 + y + y = 15 ←Combine like terms
2y + 3 = 15 ←take away 3 from both sides
-3 -3
2y = 12 ←Divide by 2 on both side to get 1 y
÷2 ÷2
y = 6
Now we know y =6, substitute it into equation 1 to find x
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Substitute y = 6 into equation 1 to find x
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x + y = 15 ←Substitute y = 6
x + 6 = 15 ←take away 6 from both sides
-6 -6
x = 9
Now we know x = 9
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Find the two numbers
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first number = x = 9
second number = y = 6
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Answer: The two numbers are 9 and 6
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