SOLUTION: the greater of two numbers is 1 more than twice the smaller. three times the greater exceeds five times the smaller by 10. find the numbers

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Question 392228: the greater of two numbers is 1 more than twice the smaller. three times the greater exceeds five times the smaller by 10. find the numbers

Answer by MathLover1(20850) About Me  (Show Source):
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the greater of two numbers is 1 more than twice the smaller. three times the greater exceeds five times the smaller by 10. find the numbers

let numbers be x and y, and let x%3Cy
given:
he greater of two numbers is 1more than twice the smaller; so,we will have

y+=+2x+%2B+1........................(1)

three times the greater exceeds five times the smaller by 10

3y+=+5x+%2B+10........................(2)

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solve a system

y+=+2x+%2B+1........................(1)
3y+=+5x+%2B+10........................(2)
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y+=+2x+%2B+1........................(1).......substitute y in.....(2)

3%282x+%2B+1%29+=+5x+%2B+10........................(2)...solve for x

6x+%2B+3+=+5x+%2B+10

6x+-+5x+=+10+-++3

x+=+7........................now find y

y+=+2x+%2B+1........................(1).substitute x

y+=+2%2A7+%2B+1

y+=+14%2B+1
y+=+15

the numbers are: x+=+7 and y+=+15