Question 124548
{{{1/4X + 1/3y = 5}}}
{{{x - y = 6}}}
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Are you sure you have this problem written correctly? Could it be:
{{{1/4}}}x + {{{1/3}}}y = 5
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GEt rid of the denominators by multiplying equation by 12
12*{{{1/4}}}x + 12*{{{1/3}}}y = 12(5)
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Cancel the denominators and you have:
3x + 4y = 60
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Multiply the 1st equation (x-y=6), by 4 and add to the above equation
3x + 4y = 60
4x - 4y = 24
---------------- adding eliminates y
7x + 0y = 84
7x = 84
x = {{{84/7}}}; divided both sides by 7
x = 12
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Find y using x - y = 6; substitute 12 for y
12 - y = 6
-y = 6 - 12
-y = -6
y = +6; multiplied equation by -1 to get rid of the negatives
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Now let's check our solutions in the original equations:
{{{1/4}}}*12 + {{{1/3}}}*6 = 5
   3   +  2  = 5; confirms our solution
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Did this unconfuse you? Any questions?