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