Solution Of System Of Linear Inequalities In Two Variables

The correct answer is option (D) : 18

The correct answer is (B) : λ = -7


But at λ = 7, D_x = D_y = D_z = 0
P₁ : 2x + 3y – z = –2
P₂ :x + y + z = 4
P₃ :x – y + |λ|z = 4λ – 4
So clearly, 5P₂ – 2P₁ = P₃, so at λ = 7, system of equation is having infinite solutions.
Therefore, λ = –7 is correct answer.

The correct option is (C): 7

Step 1: Eliminate and

Multiply equation (i) by 10 and equation (ii) by 21, then subtract both from equation (iii):

Expand and simplify:

Subtracting, we get:

Which simplifies to:

Step 2: Solve for

Equating the coefficient of , we have:

Solving for :

Step 3: Solve for

Substitute into the simplified equation:

Which simplifies to:

Solving for :

Step 4: Verify the final condition

Check if the condition is satisfied:

The condition is satisfied.

Final Answer

The values are: