SOLUTION: well there is this math word problem that i do not not understand. The word problem is this:The sum of two numbers is 8 less than twice the first number. Their difference is 4 less

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Question 501144: well there is this math word problem that i do not not understand. The word problem is this:The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number? I have no idea. Can you please explain how to get put this question into mathematical terms and how to solve to get the right answer. Thank you, please answer back as soon as possible.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the 1st number a
Call the 2nd number b
given:
(1) +a+%2B+b+=+2a+-+8+ ( The sum of two numbers is 8 less than twice the first number )
(2) +a+-+b+=+2b+-+4+ ( Their difference is 4 less than twice the second number )
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Two or more equations is called a "system" of equations.
In order to solve, the number of equations has to equal
the number of unknowns. You have 2 equations and
2 unknowns, so it's solvable.
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(1) +a+%2B+b+=+2a+-+8+
Subtract +2a+ from both sides
(1) +b+-+a+=+-8+
and
(2) +a+-+b+=+2b+-+4+
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Adding (1) and (2),
+0+=+-8+%2B+2b+-+4+
Add +12+ to both sides
+2b+=+8+%2B+4+
+2b+=+12+
+b+=+6+
and, since,
+b+-+a+=+-8+
+6+-+a+=+-8+
Add 8 to both sides
+14+-+a+=+0+
Add a to both sides
+a+=+14+
The numbers are 14 and 6
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Note that for equation (2), if I had said
(2) +b+-+a+=+2b+-+4+, I end up with negative answers,
so I avoided that.