Consistent and Dependent Systems x - 2y = 4 x + 3y = -2 This system is:  a.  consistent independent                        b.  consistent dependent                      ...

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aruv's profile pic

Posted on



This syetem of equations is consistent if


Thus in the given system of equations,




`=>`  System of equations is consistent.

Option A is corrct choice.

llltkl's profile pic

Posted on

`x - 2y = 4` ...............(i)

`x + 3y = -2` ...............(ii)

From (i) we get:

`x=2y+4` .............(iii)

Substituting the value of x in equation (ii) we get:


`rArr 5y=-6`

`rArr y=-6/5`

Putting the value of y in (iii) we get:


Hence, the solution is `(8/5,-6/5)` or `(1.6,-1.2)` .

Since, the system of equations has a single solution or one ordered pair that is a solution to both equations, it is a consistent independent system.

The graphical solution is the intersecting point of the two straight lines.

The red line represents equation (i) and the blue line equation (ii), both intersecting at a single point (1.6,-1.2).

Therefore, the correct answer is option a.  consistent independent.



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