Let's do this question, find the coordinates of 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.
All right.
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Give it a try and then let's do it together.
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We're back.
I hope you have given it a try.
Now, over here, you can see that you have two equations, right?
And we have seen that these represent a line.
Right.
This is a line and this is a line now to find the point of intersection of these two lines is the same
as solving these two equations.
Now, over here, you can see that if you just look at it in terms of equations, you have two equations
and two variables so you can solve it.
Now, in terms of geometry, these will be two lines and there will be a point where these two are intersecting.
And that is the point where both the lines are intersecting right at that point of intersection will
be a solution to both equations.
All right.
Now let's proceed in solving this equation.
We have three X plus four Y minus six is equal to zero and two X plus three Y minus 10 is equal to zero.
All right.
Now, let's multiply this equation throughout with two and I get six X plus eight Y minus 12 is equal
to zero.
Now, let's multiply this equation over here throughout with three and I get six X plus nine Y minus
30 is equal to zero.
Now can you see why I've done this?
I have done it so that I get the same number over here.
Right.
Three in the two gives me six and two in the three also gives me six.
I want to eliminate this variable.
That's why I've done this.
Now just subtract this minus this.
So when you do that eight Y minus nine Y gives you minus five and minus 12, minus minus 30 gives you
eighteen to minus Y, plus 18 is equal to zero, or it means that Y is equal to 18.
Now once you have found this substitute this value in any one of the equations, so let's put it over
here.
So three X plus 18 into four minus six is equal to zero.
That means three X is equal to minus sixty six, or you get X is equal to minus twenty two.
So the correct answer over here is option C, that is X minus 22 and Y is 18.
Now this is one way of solving this question.
Now let's see one more way in which we could have solved this question.
That's by substitution.
Alright.
Now, over here you have equation one, an equation to write.
These two represent a line.
Now, let's try whether this option fits in to this equation.
That is we are checking with a three comma zero is a valid solution of line one.
Now over here, when you substitute three comma zero, you get nine plus zero minus six.
Right.
And that is not equal to zero.
Right.
Three in the three is a nine zero in two four.
That's zero minus six now.
Nine zero minus six is three.
That's not equal to zero.
Therefore, this point does not lie on this line.
Therefore it's not the correct answer.
What about option two?
Let's try substituting two zero in both these equations.
You see that it's part of line one, right?
Because six plus zero minus six is equal to zero two zero is a point that lies on line one.
But when you substituted into line two, you get four plus minus ten and that is not equal to zero,
therefore to zero does not lie on line two.
So this is not the correct answer.
What about option C?
When you substituted into line one, you get three in two minus 22, plus four in the eighteen minus
six.
That's equal to zero.
Right.
So therefore minus twenty two eighteen is lying on line one.
Now let's substitute it into line two.
All right, doing the minus 22, plus three in the 18, minus 10, that is also equal to zero.
Therefore, this point over here lies on line one as well as line two.
And that means that this is the point of intersection of line one and line to.