Question 107316
{{{7x/11-y/6=29/33}}}
{{{2x/5-y/3=4/15}}}
Whenever I have a fraction problem, I get rid of the denominators by multiplying by the product of the denominator or LCD, whichever's easier.
Multiply the first equation by 66, second equation by 15.  
{{{66(7x/11-y/6)=66(29/33)}}}
1.{{{42x-11y=58)}}}
{{{15(2x/5-y/3)=15(4/15)}}}
2.{{{6x-5y=4}}}
Now use 2 to get y in terms of x.
2.{{{6x-5y=4}}}
{{{6x-5y=4}}}
{{{6x-4=5y}}}
{{{6x/5-4/5=y}}}
{{{y=6x/5-4/5}}}
Substitute that value for y in equation 1,
1.{{{42x-11y=58)}}}
{{{42x-11(6x/5-4/5)=58)}}}
{{{42x-66x/5+44/5=58)}}}
{{{210x/5-66x/5+44/5=290/5)}}} Change to same denominator. 
{{{144x/5=246/5)}}}
{{{x=246/144}}}
{{{x=41/24}}}Simplify to lowest terms. 
Now you can find y, 
{{{y=6x/5-4/5}}}
{{{y=(6/5)*(41/24)-4/5}}}
{{{y=(41/20)-16/20}}}
{{{y=5/4}}}
Check your answers.
{{{7x/11-y/6=29/33}}} Use your first equation. 
{{{(7/11)(41/24)-(1/6)(5/4)=29/33}}}
{{{287/264-5/24=29/33}}}
{{{(24/24)*(287/264)-(264/264)*(5/24)=29/33}}}Change to same denominator. 
{{{6888/6336-1320/6336=29/33}}}
{{{5568/6336=29/33}}}
{{{(cross(192)*29)/(cross(192)*33)=29/33}}}
{{{29/33=29/33}}}
True statement, good answer.
x=41/24(1.71), y=5/4(1.25)
{{{ graph( 300, 300, -1, 4, -1, 4, 6x/5-4/5, 42*x/11-6*29/33) }}}