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.

The substitutions are $x = \frac{91}{6}$, $y = \frac{1}{6}$.

$$X Y = \frac{91}{36}$$

Solve $7 x + 5 y = 107$ for $x$. $$x = \frac{107}{7} - \frac{5 y}{7}$$

Substitute $\frac{107}{7} - \frac{5 y}{7}$ for $x$ in $5 x + 7 y = 77$ and simplify. $$\begin{aligned}5 x + 7 y &= 77 \\ 5 \left(\frac{107}{7} - \frac{5 y}{7}\right) + 7 y &= 77 \\ y &= \frac{1}{6} \end{aligned}$$

Use substitution of the numerical value of $y$ to get the values of $x$. $$\begin{aligned}x &= \frac{107}{7} - \frac{5 y}{7} \\ x &= - \frac{1 \cdot 5}{6 \cdot 7} + \frac{107}{7} \\ x &= \frac{91}{6}\end{aligned}$$

By substituting these values into the expression, we find that:$$\begin{aligned} X Y &= \frac{91}{6} \cdot \frac{1}{6}\\ &=\frac{91}{36}\end{aligned}$$