1. **State the problem:** We are given the system of linear equations: $$50x + 49y = c$$ $$49x - 50y = c$$ where $c$ is a positive constant. We need to find the point $(x,y)$ where these two lines intersect. 2. **Use the method of solving linear systems:** To find the intersection, solve the system simultaneously. We can use the method of addition or substitution. 3. **Add the two equations:** $$ (50x + 49y) + (49x - 50y) = c + c $$ $$ 50x + 49x + 49y - 50y = 2c $$ $$ 99x - y = 2c $$ 4. **Express $y$ in terms of $x$ and $c$:** $$ y = 99x - 2c $$ 5. **Substitute $y$ back into the first equation:** $$ 50x + 49(99x - 2c) = c $$ $$ 50x + 4851x - 98c = c $$ $$ 4901x = c + 98c $$ $$ 4901x = 99c $$ $$ x = \frac{99c}{4901} $$ 6. **Find $y$ using $x$:** $$ y = 99\left(\frac{99c}{4901}\right) - 2c = \frac{9801c}{4901} - 2c $$ $$ y = c\left(\frac{9801}{4901} - 2\right) = c\left(\frac{9801 - 9802}{4901}\right) = -\frac{c}{4901} $$ 7. **Final intersection point:** $$ \left(\frac{99c}{4901}, -\frac{c}{4901}\right) $$ This point is the intersection of the two lines for any positive $c$. **Note:** The point $\left(c, \frac{c}{99}\right)$ mentioned in the problem does not satisfy both equations simultaneously, so it cannot be the intersection point.