peachyio peachyio
  • 10-01-2021
  • Mathematics
contestada

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

Respuesta :

DFGauss
DFGauss DFGauss
  • 10-01-2021

Step-by-step explanation:

(m - 2)x + y = 2

y = -(m - 2)x + 2

8 = -(m - 2)(2) + 2

6 = -(m - 2)(2)

3 = -(m - 2)

-3 = m - 2

-1 = m

mx + 2y = k

2y = -mx + k

[tex]y = - \frac{1}{2} mx + \frac{k}{2} \\ y = \frac{1}{2} x + \frac{k}{2} \\ 8 = \frac{1}{2} (2) + \frac{k}{2} \\ 7 = \frac{k}{2} \\ 14 = k[/tex]

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