Select all that apply) Which of the following are underdetermined systems?3a+b−6c=−102a+b−5c=−82x+y+3z=12x+6y+8z=36x+8y+18z=5p+q=1p+q+r=2p−q+r=1p−r=36a+8b+7c+3d=73a+5b+4c+d=8x−y=2x+y=42x+y=8Submit

An underdetermined system is a system of linear equations in which there are fewer equations than unknowns. This means that there are infinitely many solutions.

Let's analyze each system:

1. 3a+b−6c=−10 and 2a+b−5c=−8: This system has 3 unknowns (a, b, c) and 2 equations. Therefore, it is underdetermined.

2. 2x+y+3z=1, 2x+6y+8z=3, and 6x+8y+18z=5: This system has 3 unknowns (x, y, z) and 3 equations. Therefore, it is not underdetermined.

3. p+q=1, p+q+r=2, p−q+r=1, and p−r=3: This system has 3 unknowns (p, q, r) and 4 equations. Therefore, it is not underdetermined.

4. 6a+8b+7c+3d=7 and 3a+5b+4c+d=8: This system has 4 unknowns (a, b, c, d) and 2 equations. Therefore, it is underdetermined.

5. x−y=2, x+y=4, and 2x+y=8: This system has 2 unknowns (x, y) and 3 equations. Therefore, it is not underdetermined.

So, the underdetermined systems are:

• 3a+b−6c=−10 and 2a+b−5c=−8
• 6a+8b+7c+3d=7 and 3a+5b+4c+d=8