If (k, 3) is the point of intersection of the lines represented by x + py = 6 and $x = 15$ then (k, p) will be :

Step 1: Substitute the x-coordinate

We are given that the point of intersection is $(k, 3)$. This means that when $x=k$ and $y=3$, both equations are satisfied. From the second equation, $x=15$, we can directly find the value of $k$.

Step 2: Determine the value of k

Since the $x$ -coordinate of the intersection point is $k$ and the second line is $x=15$, it implies that $k$ must be equal to $15$.

Step 3: Substitute k and y into the first equation

Now that we know $k=15$ and the $y$ -coordinate of the intersection point is $3$, we can substitute these values into the first equation, $x + py = 6$, to find the value of $p$.

Step 4: Solve for p

Simplify the equation and solve for $p$. Subtract $15$ from both sides, then divide by $3$ to isolate $p$.

Step 5: State the final coordinates (k, p)

We have found $k=15$ and $p=-3$. Therefore, the ordered pair $(k, p)$ is $(15, -3)$.

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