1) The system is consistent and independent.
2) The system is inconsistent.
3) The system is inconsistent.
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.