SOLUTION: find two integers such that three times the larger minus four times the smaller is 7 and the larger is one less than two times the smaller

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Question 225069: find two integers such that three times the larger minus four times the smaller is 7 and the larger is one less than two times the smaller
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two integers, x & y; (x is larger)
:
Write an equation for each phrase:
:
"two integers such that three times the larger minus four times the smaller is 7"
3x - 4y = 7
:
"the larger is one less than two times the smaller"
x = 2y - 1
:
Use the above equation for substitution in the 1st equation; replace x:
3(2y-1) - 4y = 7
6y - 3 - 4y = 7
6y - 4y = 7 + 3
2y = 10
y = 5
:
Find x:
x = 2y -1
x = 2(5) = 1
x = 9
:
:
Check solution in the 1st statement
"find two integers such that three times the larger minus four times the smaller is 7 "
3(9) - 4(5) = 7
27 - 20 = 7