SOLUTION: One number is 1 more than 2 times another. Their product is 7 more than 3 times their sum. Find the numbers.

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Question 765198: One number is 1 more than 2 times another. Their product is 7 more than 3 times their sum. Find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
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One number is 1 more than 2 times another. Their product is 7 more than 3 times their sum. Find the numbers.
let one number be x and another numbery
if one number is 1 more than 2 times another, then we have
x=2y......eq.1
if their product is 7 more than 3 times their sum, then we have
xy=3%28x%2By%29%2B7......eq.2
solve the system:
x=2y......eq.1
xy=3%28x%2By%29%2B7......eq.2
____________________
xy=3%28x%2By%29%2B7......eq.2....substitute x from eq.1
2y%2Ay=3%282y%2By%29%2B7.......solve for y
2y%5E2=6y%2B3y%2B7
2y%5E2=9y%2B7
2y%5E2-9y-7=0

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%2A2%2A%28-7%29+%29%29%2F%282%2A2%29+
y+=+%289+%2B-+sqrt%28+81%2B56+%29%29%2F4+
y+=+%289+%2B-+sqrt%28+137%29%29%2F4+
y+=+%289+%2B-+11.7%29%2F4+
solutions:
y+=+%289+%2B+11.7%29%2F4+
y+=20.7%2F4+
y+=5.175+

y+=+%289+-11.7%29%2F4+
y+=-2.7%2F4+
y+=-0.675+
the x is
x=2%2A5.175=>x=10.35
x=2%2A%28-0.675%29=>x=-1.35
so, numbers are:
x=10.35 and y+=5.175+
or
x=-1.35 and y+=-0.675+
check:
x=2y......eq.1
10.35=2%2A5.175
10.35=10.35
xy=3%28x%2By%29%2B7......eq.2
10.35%2A5.175=3%2810.35%2B5.175%29%2B7
53.56125=3%2815.525%29%2B7
53.56125=46.575%2B7
53.56125=53.575...both rounded to one decimal are
53.6=53.6