Yes, that is correct! Well, done!

(It took me a moment to figure out where that "r" came from!)

You don't say if you did that by row-reducing the augmented matrix but here's how I did it.

The augmented matrix is

Divide the first row by 2, add the original first row to the second row, and subtract the original first row times 4 from the third row to get

Divide the second row by 7, add the original second row to the third row, and subtract thenewsecond row from the first row to get

.

The fact that the last row consists of all "0"s tells us that we will have an infinite number of solutions. From the first equation, so and so . Now let r= z to get your soltutions.