1) The system is <u>consistent and independent</u>.
2) The system is <u>inconsistent</u>.
3) The system is <u>inconsistent</u>.
<u>Step-by-step explanation</u>:
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
<u>2x + y = 1</u>
<u>4x = 4</u>
∴ 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 <u>consistent and independent</u>.
2)
2x - y = 3
-4x + 2y = -6
Mulitply the 1st equation with 2 on both sides,
4x - 2y = 6
<u>-4x + 2y = -6</u>
<u> 0 </u>
The system of equation has no solution.
The system is <u>inconsistent</u>.
3)
2x - y = 3 , multiply by 2 on both sides.
we get, 4x - 2y = 6
<u>-4x +2y = 6</u>
<u> 0 </u>
The system of equation has no solution.
The system is <u>inconsistent</u>.
