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In this lesson, we will learn how to identify inconsistent systems of equations in three variables.

Q1:

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?

Q2:

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

Q3:

Q4:

Q5:

Find the value of π that would make the equations 4 π₯ + 9 π¦ + 5 π§ = 0 , 1 6 π₯ + 3 6 π¦ + π π§ = 0 , and 9 π₯ β 8 π¦ β 3 π§ = 0 have a solution other than zero.

Q6:

Find the value of π that would make the equations β 5 π₯ β 3 π¦ + 9 π§ = 0 , β 2 0 π₯ β 1 2 π¦ + π π§ = 0 , and 2 π₯ + 3 π¦ + 3 π§ = 0 have a solution other than zero.

Q7:

Find the value of π that would make the equations β 6 π₯ + 4 π¦ + 3 π§ = 0 , β 1 2 π₯ + 8 π¦ + π π§ = 0 , and β 8 π₯ β 2 π¦ β 4 π§ = 0 have a solution other than zero.

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