Math Problem Solver

The system of linear equations has exactly one solution.

The substitutions are \( x = \frac{73}{23} \), \( y = \frac{49}{23} \).

\[x - y = \frac{24}{23}\]

Solve \(2 x + 5 y = 17\) for \(x\). \[x = \frac{17}{2} - \frac{5 y}{2}\]

Substitute \(\frac{17}{2} - \frac{5 y}{2}\) for \(x\) in \(3 x - 4 y = 1\) and simplify. $$\begin{aligned}3 x - 4 y &= 1 \\ 3 \left(\frac{17}{2} - \frac{5 y}{2}\right) - 4 y &= 1 \\ y &= \frac{49}{23} \end{aligned}$$

Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{17}{2} - \frac{5 y}{2} \\ x &= - \frac{5 \cdot 49}{2 \cdot 23} + \frac{17}{2} \\ x &= \frac{73}{23}\end{aligned}$$

By substituting these values into the expression, we find that:$$\begin{aligned} x - y &= \frac{73}{23} - \frac{49}{23}\\ &=\frac{24}{23}\end{aligned}$$