If the system of linear equations array l x + y + z = 4 2x + y - z = 3 3x + 2y = k array has infinitely many solutions, and (x₀, y₀, 2) is a solution of this system, then the value of k + x₀ + y₀ is equal to

Step-by-step solution

For the system to have infinitely many solutions, the determinant of the coefficient matrix must be zero, and the augmented matrices must also have zero determinants. This implies that one equation is a linear combination of the other two. Observing the coefficients of x , y , and z , we can see that the third row is the sum of the first two rows: (x + y + z) + (2x + y - z) = 3x + 2y For the system to be consistent and have infinitely many solutions, the same linear combination must apply to the constant terms. The