Question

The lines (m-2)x+y=2 and mx+2y=k intersect at (2,8). Find the values of m and k

Answer 1

m = - 1, k = 14

Explanation:

The coordinates of the point of intersection (2, 8 ) satisfy both equations.

Substitute x = 2, y = 8 into the equations and solve for m and k

(m - 2)x + y = 2

2(m - 2) + 8 = 2

2m - 4 + 8 = 2

2m + 4 = 2 ( subtract 4 from both sides )

2m = - 2 ( divide both sides by 2 )

m = - 1

and

mx + 2y = k

- 1(2) + 2(8) = k

- 2 + 16 = k

14 = k

Then m = - 1 and k = 14