Question

Write the parametric representation of the solution of each linear equation. 31. 3x – 6y = 33 32. 3x 2y 2z = 3

Answer 1

The parametric representations for the linear equations 3x - 6y = 33 and 3x + 2y + 2z = 3 are, respectively, x = t, y = (3/2)t - 11 and x = t, y = s, z = (3 - 3t - 2s)/2.

Step-by-step explanation:

To write the parametric representations for the equations 3x − 6y = 33 and 3x + 2y + 2z = 3, we can express one of the variables in terms of a parameter, typically t, and solve for the others accordingly.

For the first equation 3x − 6y = 33, we can let x = t (where t is a parameter) and solve for y:

3t − 6y = 33
y = ½ (3t − 33)
y = ½ (3t) − ½ (33)
y = ½(3)t − 11

So the parametric equations for x and y are:

• x = t
• y = ½(3)t − 11

For the second equation 3x + 2y + 2z = 3, we can let x = t and y = s (where t and s are parameters), then solve for z:

3t + 2s + 2z = 3
2z = 3 − 3t − 2s
z = ½ (3 − 3t − 2s)

So the parametric equations for x, y, and z are:

• x = t
• y = s
• z = ½ (3 − 3t − 2s)