ANSWER
[tex]( \frac{2}{3} , \frac{1}{5} )[/tex]
EXPLANATION
The first equation is
[tex] \frac{1}{2} x - \frac{3}{4} y = \frac{11}{60} ...(1)[/tex]
The second equation is
[tex] \frac{2}{5} x + \frac{1}{6} y = \frac{3}{10} ...(2)[/tex]
We want to eliminate y, so we multiply the first equation by
[tex] \frac{4}{5} [/tex]
[tex] \frac{4}{5} \times \frac{1}{2} x - \frac{4}{5} \times \frac{3}{4} y = \frac{11}{60} \times \frac{4}{5} [/tex]
[tex]\frac{2}{5} x - \frac{3}{5} y = \frac{11}{75} ...(3)[/tex]
We now subtract equation (3) from (2)
[tex] (\frac{2}{3} x - \frac{2}{3} x )+ ( \frac{1}{6} y - - \frac{3}{5}y ) =( \frac{3}{10} - \frac{11}{75} )[/tex]
[tex] \frac{1}{6} y + \frac{3}{5}y =\frac{3}{10} - \frac{11}{75} [/tex]
[tex] \frac{23}{30}y = \frac{23}{150} [/tex]
Multiply both sides by
[tex] \frac{30}{23} [/tex]
[tex] \implies \: \frac{30}{23} \times \frac{23}{30}y= \frac{23}{150} \times \frac{30}{23}[/tex]
[tex] \implies \: y = \frac{1}{5} [/tex]
Substitute into the first equation to solve for x .
[tex]\frac{1}{2} x - \frac{3}{4} \times \frac{1}{5} = \frac{11}{60}[/tex]
Multiply to obtain
[tex]\frac{1}{2} x - \frac{3}{20} = \frac{11}{60}[/tex]
[tex]\frac{1}{2} x = \frac{11}{60} + \frac{3}{20}[/tex]
[tex]\frac{1}{2} x = \frac{1}{3} [/tex]
Multiply both sides by 2.
[tex]2 \times \frac{1}{2} x =2 \times \frac{1}{3} [/tex]
[tex]x = \frac{2}{3} [/tex]
The solution is
[tex]( \frac{2}{3} , \frac{1}{5} )[/tex]
