Math Problem Solver

Assuming \(x\) and \(X\) are referring to the same variable.

Assuming \(y\) and \(Y\) are referring to the same variable.

The system of linear equations has exactly one solution.

\[x = \frac{170000}{3}\]

\[y = - \frac{350000}{9}\]

Solve \(\frac{x}{2} + \frac{3 y}{5} = 5000\) for \(x\). \[x = 10000 - \frac{6 y}{5}\]

Substitute \(10000 - \frac{6 y}{5}\) for \(x\) in \(\frac{11 x}{10} + \frac{3 y}{2} = 4000\) and simplify. $$\begin{aligned}\frac{11 x}{10} + \frac{3 y}{2} &= 4000 \\ \frac{11 \left(10000 - \frac{6 y}{5}\right)}{10} + \frac{3 y}{2} &= 4000 \\ y &= - \frac{350000}{9} \end{aligned}$$

Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 10000 - \frac{6 y}{5} \\ x &= 10000 - 6 \left(-350000\right) \frac{1}{9} \cdot \frac{1}{5} \\ x &= \frac{170000}{3}\end{aligned}$$