Consistent and Dependent Systems
x - 2y = 4
x + 3y = -2
This system is: a. consistent independent
b. consistent dependent
This syetem of equations is consistent if
Thus in the given system of equations,
`=>` System of equations is consistent.
Option A is corrct choice.
`x - 2y = 4` ...............(i)
`x + 3y = -2` ...............(ii)
From (i) we get:
Substituting the value of x in equation (ii) we get:
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.