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This is an urgent math problem. Online waiting
Change x+y=5k to x = 5k-y.

Change x-y=9k to x=y+9k.

Substitute these two forms of x into 2x+3y=6 respectively.

Equation set 2(5k-y)+3y=6 ... gives 1.

2(y+9k)+3y=6...2 formula

1 is simplified to 10k+y=6.

Equation 2 is simplified to 5y+ 18k=6.

Lianlide 6- 10k=(6- 18k)/5

The solution is k=3/4.