Question 578790
To add or compare fractions, you express them on a common denominator that is a multiple of all the denominators.
If you were working with 1/5 and 1/4, you would use 20 as a common denominator because it is a common multiple of 4 and 5.
When fractions present issues in an equation you "eliminate denominators by multiplying both sides of the equal sign by a common multiple, to get an simpler equivalent equation
{{{(1/5)x + (1/4)y = 2}}} --> {{{20((1/5)x + (1/4)y) = 20*2}}} --> {{{4x+5y=40}}}
You can do something similar for the other equation, using 12 for a common multiple.
{{{(1/6)x-(1/12)y=-13/6}}} --> {{{12*((1/6)x-(1/12)y)=12*(-13/6)}}} -->
{{{2x-y=-26}}}
Now you have the easier system:
{{{system(2x-y=-26,4x+5y=40)}}}
You could use substitution, solving one equation for y
{{{2x-y=-26}}} --> {{{2x+26=y}}}
and substituting the expression found for y in the other equation
{{{4x+5(2x+26)=40}}} --> {{{4x+10x+130=40}}} --> {{{14x+130=40}}} --> {{{14x=40-130}}} --> {{{14x=-90}}} --> {{{x=-90/14}}} --> {{{highlight(x=-45/7)}}}
Then substituting into {{{y=2x+26}}}
{{{y=2*(-45/7)+26}}} --> {{{y=-90/7+182/7}}} --> {{{highlight(y=92/7)}}}