Question

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Answer 1

1) The system is consistent and independent.

2) The system is inconsistent.

3) The system is inconsistent.

Step-by-step explanation:

The system of equation is said to be

inconsistent - it has no solution

consistent - it has at least one solution.

independent - it has exactly one solution

dependent - it has more than one solution.

1)

2x - y = 3

2x + y = 1

4x      =  4

∴ The value of x=1 and substitute x=1 in any of the above equations.

y = -2(1) + 1 = -1

The system of equation has one solution (x,y) = (1,-1).

The system is consistent and independent.

2)

2x - y = 3

-4x + 2y = -6

Mulitply the 1st equation with 2 on both sides,

4x - 2y = 6

-4x + 2y = -6

  0              

The system of equation has no solution.

The system is inconsistent.

3)

2x - y = 3 , multiply by 2 on both sides.

we get, 4x - 2y = 6

            -4x +2y = 6

                0            

The system of equation has no solution.

The system is inconsistent.