Worksheet: Inconsistent Systems of Equations in Three Variables

In this worksheet, we will practice identifying inconsistent systems of equations in three variables.

Q1:

Find the set of values of for which the simultaneous equations have at least one solution.

• A
• B
• C
• D
• E

Q2:

Find the value of that would make the equations , , and have a solution other than zero.

Q3:

Three numbers add up to 216. The sum of the first two numbers is 112 and the third number is 8 less than this sum. How many possible values are there for the numbers?

• A1
• B0
• Cinfinitely many

Q4:

Find the set of values of for which the simultaneous equations have at least one solution.

• A
• B
• C
• D
• E

Q5:

Find the set of values of for which the simultaneous equations have at least one solution.

• A
• B
• C
• D
• E

Q6:

Find the value of that would make the equations , , and have a solution other than zero.

Q7:

Find the value of that would make the equations , , and have a solution other than zero.