Which ordered pair is a solution to the system of linear equations (1)/(2)x-(3)/(4)y=(11)/(60) and (2)/(5)x+(1)/(6)y=(3)/(10) ? ((1)/(5),-(2)/(3)) ((1)/(5),(2)/(3)) ((2)/(3),-(1)/(5)) C ((2)/(3),(1)/(5))

To determine which ordered pair is a solution to the system of linear equations, we need to substitute each pair into both equations and see if they satisfy both equations.<br /><br />Let's start with the first pair: $(\frac {1}{5},-\frac {2}{3})$<br /><br />Substituting into the first equation:<br />$\frac {1}{2}(\frac {1}{5})-\frac {3}{4}(-\frac {2}{3})=\frac {11}{60}$<br />$\frac {1}{10}+\frac {1}{2}=\frac {11}{60}$<br />$\frac {3}{5}=\frac {11}{60}$<br /><br />This is not true, so the first pair is not a solution.<br /><br />Next, let's try the second pair: $(\frac {1}{5},\frac {2}{3})$<br /><br />Substituting into the first equation:<br />$\frac {1}{2}(\frac {1}{5})-\frac {3}{4}(\frac {2}{3})=\frac {11}{60}$<br />$\frac {1}{10}-\frac {1}{2}=\frac {11}{60}$<br />$-\frac {1}{5}=\frac {11}{60}$<br /><br />This is also not true, so the second pair is not a solution.<br /><br />Now let's try the third pair: $(\frac {2}{3},-\frac {1}{5})$<br /><br />Substituting into the first equation:<br />$\frac {1}{2}(\frac {2}{3})-\frac {3}{4}(-\frac {1}{5})=\frac {11}{60}$<br />$\frac {1}{3}+\frac {3}{20}=\frac {11}{60}$<br />$\frac {20}{60}+\frac {9}{60}=\frac {11}{60}$<br />$\frac {29}{60}=\frac {11}{60}$<br /><br />This is not true, so the third pair is not a solution.<br /><br />Finally, let's try the fourth pair: $(\frac {2}{3},\frac {1}{5})$<br /><br />Substituting into the first equation:<br />$\frac {1}{2}(\frac {2}{3})-\frac {3}{4}(\frac {1}{5})=\frac {11}{60}$<br />$\frac {1}{3}-\frac {3}{20}=\frac {11}{60}$<br />$\frac {20}{60}-\frac {9}{60}=\frac {11}{60}$<br />$\frac {11}{60}=\frac {11}{60}$<br /><br />This is true, so the fourth pair is a solution.<br /><br />Therefore, the correct answer is C $(\frac {2}{3},\frac {1}{5})$.