Question

Are these problems inconsistent?
2x+3y=2
2x-3y=6

Answer 1

I'm not too sure on the difference between consistent and inconsistent equations.

Answer 2

You typed before:
Inconsistent -- no solution
Consistent -- a single solution
Dependent -- infinite number of solution
This system has 1 solution. You can find it by elimination or substitution.

Answer 3

okay. i see.

Answer 4

Consistent -- a single solution

Just add them and then subtract them.

Answer 5

If the slope is different, then the two lines will intersect and will have one solution. They then form a Consistent and independent system with one solution.

If the slope is same, y-intercept is same, then the two lines coincide. They then form a Consistent and dependent system with infinite solutions.

If the Slope is same but different y-intercepts, then the two lines are parallel. They then form an Inconsistent system with no solution.




2x+3y=2
2x-3y=6

Putting them in slope-intercept form
2x+3y=2
3y = - 2x + 2
2 2
y = - ---- x + -----
3 3

2x-3y=6
-3y = -2x + 6
-2 6
y = ---- x + -----
-3 -3
2
y = ---- x - 2
3
since both have different slopes, hence they will intersect and have one solution.

so they form a consistent pair

Answer 6

thanks guys!