 Homework Statement

1. Find a linear equation in the variables x, y and z that has a general solution:
x = 3  4p + q
y = p
z = q
where p and q are arbitrary parameters
2. Express a general solution for the equation in part (1) in two other different ways
3. Write down a linear system of two different non zero linear equations such that the system has the same general solution as in part (1)
 Homework Equations
 Not sure
1)
x = 3  4p + q
x = 3  4y + z
x + 4y  z = 3
2) x + 4y  z = 3
(i) let x = a and y = b, so z = a + 4b  3
General solution:
x = a
y = b
z = a+ 4b  3
(ii) let x = r and z = t, so y = (3  r + t) / 4
General solution:
x = r
y = (3  r + t) / 4
z = t
3) I don't understand this part. Is the answer the same as part (1)? Can I just take random equations like x +2y = 1 and 2y  z = 2? Is this the form asked by the questions?
Thanks
x = 3  4p + q
x = 3  4y + z
x + 4y  z = 3
2) x + 4y  z = 3
(i) let x = a and y = b, so z = a + 4b  3
General solution:
x = a
y = b
z = a+ 4b  3
(ii) let x = r and z = t, so y = (3  r + t) / 4
General solution:
x = r
y = (3  r + t) / 4
z = t
3) I don't understand this part. Is the answer the same as part (1)? Can I just take random equations like x +2y = 1 and 2y  z = 2? Is this the form asked by the questions?
Thanks