First part looks OK.

Second part: Solve simultaneously:

3x - y + 4z = 3 .... (1)

4x - 2y + 7z = 8 .... (2)

There are an infinite number of solutions. One possible form for these solutions is go by letting z = t, say. Then

3x - y = 3 - 4t .... (1')

4x - 2y = 8 - 7t .... (2')

Solve (1') and (2') simultaneously to get x and y in terms of t. This soluion is the line of intersection of the two planes (written in parametric form).