Question

Which classification describes the following system of equations?

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Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which classification describes the following system of equations

5x + y + 2z = 13

4x + 3y + 6z = 17

x + 2y = 4

A) inconsistent and dependent

B) consistent and dependent

C) consistent and independent

D) inconsistent and independent

CONCEPT TO BE IMPLEMENTED

• For a given system of equations if there exists at least one solution, it is said to be consistent .

• If a consistent system has exactly one solution, it is independent .

• If a consistent system has an infinite number of solutions, it is dependent

EVALUATION

Here the given system of equations are

5x + y + 2z = 13 - - - - - (1)

4x + 3y + 6z = 17 - - - - - (2)

x + 2y = 4 - - - - - (3)

2 × Equation 1 - Equation 3 gives

9x + 4z = 22 - - - - - - (4)

2 × Equation 2 - 3 × Equation 3 gives

5x + 12z = 22 - - - - - - (5)

Again 3 × Equation 4 - Equation 5 gives

22x = 44

⇒ x = 2

From Equation 3 we get

2y = 2

⇒ y = 1

From Equation 4 we get

4z = 4

⇒ z = 1

So the solution of the system of equations is given by x = 2 , y = 1 , z = 1

Thus the given system of equations have a solution

So the given system of equations are consistent

Also the solution of the system of equations are unique

So the given system of equations is independent

FINAL ANSWER

Hence the correct option is

C) consistent and independent

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