Question 600898
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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