SOLUTION: One is 11 less than 6 times another number if their product is 7. Find the numbers

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Question 1012836: One is 11 less than 6 times another number if their product is 7. Find the numbers
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let one number be x and another number y
if one is 11 less than 6 times another number we have:

x=6y-11....eq.1
if their product is 7 we have:
x%2Ay=7....eq.2....substitute x from eq.1
%286y-11%29%2Ay=7.....solve for y
6y%5E2-11y=7
6y%5E2-11y-7=0
y=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y=+%28-%28-11%29+%2B-+sqrt%28%28-11%29%5E2-4%2A6%2A%28-7%29+%29%29%2F%282%2A6%29+
y=+%2811+%2B-+sqrt%28121%2B168+%29%29%2F12+
y=+%2811+%2B-+sqrt%28289+%29%29%2F12+
y=+%2811+%2B-+17%29%2F12+
solutions:
y=+%2811+%2B+17%29%2F12+
y=28%2F12+
highlight%28y=+7%2F3%29+
or
y=+%2811+-+17%29%2F12+
y=-6%2F12+
highlight%28y=+-1%2F2%29+
the number x will be:
x%2Ay=7....eq.2
x=7%2Fy
x=7%2F%287%2F3%29
x=%283%2A7%29%2F7
highlight%28x=3%29
or
x=7%2Fy
x=7%2F%28-1%2F2%29
x=%282%2A7%29%2F%28-1%29
highlight%28x=-14%29
so, there is two pairs of numbers and they are:
highlight%28x=3%29 and highlight%28y=+7%2F3%29+
or
highlight%28x=-14%29 and highlight%28y=+-1%2F2%29+