Use the subtraction method to solve. Find whether the equations are independent, dependent, or inconsistant.?

Question

2x - y = 4
2x - y = 3

Answer 1

    2x - y = 4
- ( 2x - y = 3 )
------------------
    0x - 0y = 1

0=1

That's inconsistent.

Answer 2

2x - y = 4..... (1)
2x - y = 3..... (2)

Subtract (2) from (1),

2x - 2x - y + y = 4 - 3
0 = 1 which is not true.

So, the system of equations is inconsistent (No solution).


If you solve a system and get an incorrect statement like 0 = 1. The system is inconsistent. If you get a true statement like 0 = 0, the system is dependent. If the system is independent, you get the values of x and y after working out.



There are criteria for consistency which help us determine the consistency of a given system of equations without solving. Here they are:

Consider the system of linear equations:

a1x + b1y + c1 = 0
a2x + b2y + c2 = 0

If the system has a unique solution:
a1/a2 does not equal b1/b2 does not equal c1/c2

If the system has no solution:
a1/a2 = b1/b2 but does not equal c1/c2

If the system has infinite solutions:
a1/a2 = b1/b2 = c1/c2

Answer 3

If we subtract one equation from the other by subtracting like terms in each equation, we get

2x-y=4
2x-y=3
-----------
0-0=1
or
0=1
This is impossible, so it is an inconsistent equation.

Answer 4

it's an inconsistant equation
because:
3 not equale to 4

Answer 5

2x - y = 4
- ( 2x - y = 3 )
------------------
0x - 0y = 1

0=1

That's inconsistent.

Answer 6

2x-y=4......(1)
2x-y=3......(2)

making x coeficients equal

(1)*+1 => +2x-y=+4
(2)* -1 => -2x+y=-3
----------------------------
0=1
----------------------------