## Elementary Algebra

$= \frac{19}{42}$
1) First, we plug in the given values, and then we simplify the fractions. 2) Find a common denominator in Step #6: multiply the first fraction by $7$ and the second fraction by $6$ to obtain a common denominator of $42$ $\frac{1}{4}x - \frac{2}{5}y$ for $x = \frac{2}{3}$, $y =-\frac{5}{7}$ $= \frac{1}{4}(\frac{2}{3}) - \frac{2}{5}(-\frac{5}{7})$ $= \frac{1(2)}{4(3)} - \frac{2(-5)}{5(7)}$ $= \frac{2}{12} - \frac{-10}{35}$ $= \frac{2}{12} + \frac{10}{35}$ $= \frac{1}{6} + \frac{2}{7}$ $= \frac{1(7)}{42} + \frac{2(6)}{42}$ $= \frac{7}{42} + \frac{12}{42}$ $= \frac{19}{42}$