State whether the following equations are independent, dependent, consistent, inconsistent and justify: 2x = 2 + 5y3x = 8 - 3y
The given system of linear equations consists of 2x = 2 + 5y
3x = 8 - 3y.
Plotting the lines represented by the two equations gives:
It is seen that the two lines intersect each other at a single unique point.
The given equations are consistent and independent.
The lines are independent.
If all you need is to know if a 2x2 system is dependent or not, and if it's consistent or not, one thing you can do is just look at each equation and see what the slope is. For the first one the slope is 2/5; for the second one the slope is -1.
So they have different slopes, they can't be dependent since they're not the same line.
And they can't be inconsistent, that would be parallel lines which have the same slope.
So they're independent and consistent.