Math Problem Solver

The system of equations has one solution.

\[x = - \frac{56}{81}, y = - \frac{88}{81}\]

By substituting these values into the expression, we find that: $$\begin{aligned}- x + y &= - \frac{32}{81}\end{aligned}$$

Solve \(4 x - 5 y = \frac{8}{3}\) for \(x\). \[x = \frac{5 y}{4} + \frac{2}{3}\]Substitute \(\frac{5 y}{4} + \frac{2}{3}\) for \(x\) in \(\frac{3 x}{2 y} = \frac{21}{22}\) and simplify. $$\begin{aligned}\frac{3 x}{2 y} &= \frac{21}{22} \\ \frac{3 \left(\frac{5 y}{4} + \frac{2}{3}\right)}{2 y} &= \frac{21}{22} \\ \frac{15}{8} + \frac{1}{y} &= \frac{21}{22} \end{aligned}$$Substitute \(- \frac{88}{81}\) into \(4 x - 5 y = \frac{8}{3}\) to solve for \(x\). \[\begin{aligned}4 x + \frac{440}{81} &= \frac{8}{3}\\4 x &= - \frac{224}{81}\\x &= - \frac{56}{81}\end{aligned}\]This yields the following solution. $$\begin{aligned}x = - \frac{56}{81},\,y = - \frac{88}{81}\end{aligned}$$

By substituting these values into the expression, we find that: $$\begin{aligned}- x + y &= - \frac{32}{81}\end{aligned}$$