-2x - 3y +2=-1
-2x + y = 8
x + 3y + 5z = -2

Except -1 for all real values of k given the equations has a unique solution.

Step-by-step explanation:

Except -1 for all real values of k given the equations has a unique solution.

Explanation:

Compare given linear pair of equations

(3k+1)x+3y-2 = 0 (1)

(k²+1)x+(k-2)y-5=0 (2)

with

(2)

(3)

we get ,

and

\* Given linear equations have unique solution *\

=> 3k(k-2)+1(k-2)≠3k²+3

=> 3k²-6k+k-2≠3k²+3

=> 3k²-5k-3k²≠3+2

=> -5k ≠ 5

Divide each term by (-5) , we get

=> k ≠-1

Therefore,

Except -1 for all real values of k given the equations has a unique solution.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: