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Let's do this question, find the coordinates of the point of intersection of three X plus four Y minus

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six is equal to zero and two X plus three Y minus 10 is equal to zero.

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All right.

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What's the video?

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Give it a try and then let's do it together.

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All right.

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We're back.

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I hope you have given it a try.

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Now, over here, you can see that you have two equations, right?

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And we have seen that these represent a line.

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Right.

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This is a line and this is a line now to find the point of intersection of these two lines is the same

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as solving these two equations.

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Now, over here, you can see that if you just look at it in terms of equations, you have two equations

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and two variables so you can solve it.

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Now, in terms of geometry, these will be two lines and there will be a point where these two are intersecting.

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And that is the point where both the lines are intersecting right at that point of intersection will

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be a solution to both equations.

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All right.

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Now let's proceed in solving this equation.

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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.

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All right.

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Now, let's multiply this equation throughout with two and I get six X plus eight Y minus 12 is equal

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to zero.

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Now, let's multiply this equation over here throughout with three and I get six X plus nine Y minus

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30 is equal to zero.

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Now can you see why I've done this?

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I have done it so that I get the same number over here.

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Right.

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Three in the two gives me six and two in the three also gives me six.

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I want to eliminate this variable.

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That's why I've done this.

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Now just subtract this minus this.

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So when you do that eight Y minus nine Y gives you minus five and minus 12, minus minus 30 gives you

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eighteen to minus Y, plus 18 is equal to zero, or it means that Y is equal to 18.

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Now once you have found this substitute this value in any one of the equations, so let's put it over

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here.

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So three X plus 18 into four minus six is equal to zero.

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That means three X is equal to minus sixty six, or you get X is equal to minus twenty two.

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So the correct answer over here is option C, that is X minus 22 and Y is 18.

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Now this is one way of solving this question.

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Now let's see one more way in which we could have solved this question.

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That's by substitution.

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Alright.

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Now, over here you have equation one, an equation to write.

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These two represent a line.

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Now, let's try whether this option fits in to this equation.

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That is we are checking with a three comma zero is a valid solution of line one.

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Now over here, when you substitute three comma zero, you get nine plus zero minus six.

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Right.

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And that is not equal to zero.

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Right.

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Three in the three is a nine zero in two four.

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That's zero minus six now.

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Nine zero minus six is three.

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That's not equal to zero.

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Therefore, this point does not lie on this line.

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Therefore it's not the correct answer.

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What about option two?

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Let's try substituting two zero in both these equations.

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You see that it's part of line one, right?

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Because six plus zero minus six is equal to zero two zero is a point that lies on line one.

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But when you substituted into line two, you get four plus minus ten and that is not equal to zero,

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therefore to zero does not lie on line two.

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So this is not the correct answer.

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What about option C?

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When you substituted into line one, you get three in two minus 22, plus four in the eighteen minus

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six.

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That's equal to zero.

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Right.

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So therefore minus twenty two eighteen is lying on line one.

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Now let's substitute it into line two.

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All right, doing the minus 22, plus three in the 18, minus 10, that is also equal to zero.

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Therefore, this point over here lies on line one as well as line two.

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And that means that this is the point of intersection of line one and line to.