Let's do this question, the point of intersection of three X plus four Y minus six is equal to zero
and two X plus three Y minus 10 is equal to zero is in whether it's in the 1st Squadron, 2nd Squadron,
3rd or 4th Quadrant.
All right.
Pause the video, give it a try and then let's do it together.
All right.
We're back.
Let's do it together.
Remember, the X Y plane is divided into four quadrants, right?
This is the first quadrant.
This is the second quadrant.
This is the third quadrant.
And this is the fourth quadrant.
All right.
Over here, we are given two lines.
This is line one and this is line two right now.
One way of solving this question is you can solve these two given equations.
And if you find the point of intersection, you can find in which quadrant that point lies, the other
ways you just need to plot these equations in an approximate manner.
And looking at the slope and the way the line is, you can identify where the point of intersection
can be.
So that is much faster.
Let's try to find it out using that method.
All right.
So over here I have my x axis and this is my Y axis.
Now, let's plot the first line over here.
That's three X plus four Y, minus six is equal to zero.
Now, the plot, this line, I just need two points right now.
Let's substitute X is equal to zero.
When X is equal to zero.
This becomes or Y minus six is equal to zero.
Right.
That is why is equal to three by two.
Therefore one point would be zero.
Three by two.
Right now let's put Y is equal to zero.
When Y is equal to zero we get three, X minus six is equal to zero or X is equal to two.
That is to zero is also one more point.
So we have two points over here.
Let's plot these two points.
This is zero three by two and this is two zero.
Now let's draw a line that's passing through these two points.
All right, so this is the line one which is given to us now, let's put X is equal to zero into this
equation.
So we get three, Y is equal to 10, or Y is ten by three.
Right.
And let's put.
Why is equal to zero?
Into this equation that gives us two X equal to 10.
That is X is equal to five.
So the second point would be five zero.
Let's plot these two points.
But this is five zero and this is zero ten by three.
Let's join these two points and draw a line.
So this is the line.
And now looking at this, you can easily understand that these two lines are going to intersect in this
second quadrant right over here.
The distance is reducing over here.
The distance between them is increasing.
So they are going to intersect over here.
That's the second quadrant.