SOLUTION: May I ask a Question? What is the equation for finding the point of intersection, given the equations of two lines that intersect? Like: Find the point in which the lines y= x+

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Question 600898: May I ask a Question?
What is the equation for finding the point of intersection, given the equations of two lines that intersect?
Like: Find the point in which the lines y= x+4 and 3x+2y=13.
Thank you ma'am/sir.
Answer by Nihal@SriLanka(22) (Show Source):
You can put this solution on YOUR website!
For lines to intersect they must have a common point (the point of intersection) and at this point the x and y values representing the coordinates of the point must satisfy both equations representing the lines.

In the present case, if there is a point of intersection its coordinates (x,y) must satisfy both equations y=x+4 and 3x+2y=13.

Now we proceed to solve these equations for x and y.

Multiplying both sides of the first equation by 2 we have 2y=2x+8
Substituting 2x+8 for 2y in the second equation we have 3x+(2x+8)=13
i.e. 3x+2x=13-8
i.e. 5x =5
i.e. x = 1

Now substituting x= 1 in the first equation we have y=1+4=5

We conclude that (1,5) is the point of intersection of the given lines.

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