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Home Q & A Board Science-Related Homework Help Mathematics
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julian2ham julian2ham
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11 years ago
I understand how elimination works, the thing is that we haven't had experience with fractions, for example:
{4x-9y=-60
{1/3x-3/4y= -5

How would I go about this?
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#1
11 years ago
clear the fractions first by multiplying by 12 which is the LCD

You get 4x - 9y = -60 for the second equation. Since it is the same as the first, these two lines coincide and there are an infinite # of answers.
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#2
11 years ago
i don't actually think you can use elimination on fractions unless by some magical thingy when you multiply the 2nd fraction it will turn into something like the square of the first + something else
1/3x-3/4y=-5
4y-9x=-60xy(impossible to eliminate because of the xy not just x or y)
the easiest way to solve it it so take x from the first
x=(-60+9y)/4
replace in the 2nd and you'll have an equation for y
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#3
11 years ago
One way to solve problems like this is first to multiply each equation through by the least common denominator and then to proceed as usual from there.  In the example you gave, this means multiplying everything in the bottom equation by 12, giving
4x - 9y = -60
which is now the same as the top equation.  Because your equations are dependent, you don't have an infinite number of solutions: once you pick any value of x, you can find a value of y that will work by solving the equation 4x - 9y = -60 for y.
wrote...
#4
11 years ago
solve for 4x-9y=-60 in terms of y
y = 4/9x + 20/3
plug that into the second equation where you find the term y:
1/3x - 3/4(4/9x +20/3)=-5
and solve:
(fractions don't change just cuz they have an x... 3/4 * 4/9 = 12/36 and simplify to -1/3x) and since 1/3x - 1/3x gives you 0 it's not solvable.  And, furthermore, both equations are equivalent.  Normally this is done with dissimilar equations to solve for an intersection point... these equations are equal therefore are equal at all points.
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