In the given system of equations, $m$ and $k$ are constants. The graphs of these equations in the xy-plane intersect at the point $(5, y)$. What is the value of $m$?Equations:1) $mx + ky = -83$2) $2x + ky = 22$

Answer: The value of $m$ is $-19$.

Explanation:1. Use the point of intersection: Since the graphs intersect at $(5, y)$, this point satisfies both equations. Substitute $x = 5$ into both equations: For equation 1: $m(5) + ky = -83 \Rightarrow 5m + ky = -83$ For equation 2: $2(5) + ky = 22 \Rightarrow 10 + ky = 22$

2. Solve for $ky$ from the second modified equation: From $10 + ky = 22$: $ky = 22 - 10$ $ky = 12$

3. Substitute the value of $ky$ into the first modified equation: We have $5m + ky = -83$ and we found $ky = 12$. $5m + 12 = -83$

4. Solve for $m$: Subtract $12$ from both sides: $5m = -83 - 12$ $5m = -95$ Divide by $5$: $m = \dfrac{-95}{5}$ $m = -19$

5. Conclusion: The value of $m$ is $-19$.