Question

the line (k+2)x+5=3y and (k+3)y=2x-6 have the same gradient . find possible values of k.​

Answer 1

Answer:

K = 0, or -5

Step-by-step explanation:

1) (k+2)x+5=3y

2) (k+3)y=2x-6

First line: y = $\frac{(k+2)}{3}x +5$

Second line: y = $\frac{2}{(k+3)}x -6$

Since their gradient is the same then: $\frac{(k+2)}{3} = \frac{2}{(k+3)}$

$\left(k+2\right)\left(k+3\right)=6\\k^2+5k+6=6\\k^2+5k=0\\k = 0, k = -5$