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Jane says that she can use addition to show that the graphs of 2x - 3y = 1 and 2x + 3y = 2 are intersecting lines. In two or more complete sentences, describe the process of using addition to show that the lines are intersecting.

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In addition method, we add the two equations which will result to the elimination of one variable. Then, we can find for the solution of x and y. We do it as follows:

    2x - 3y = 1
+ 2x + 3y = 2 
---------------------
   4x          = 3
              x = 3/4
              y = 1/6

And since we have values for x and y, then they really are intersecting lines at point (3/4,1/6).

Two lines in a plane can intersect ,overlap or be parallel.When two lines intersect they have a common point which lies on both line .This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses  Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.

2x - 3y = 1

+ 2x + 3y = 2  

---------------------

4x =3 Or x= [tex] \frac{3}{4} . [/tex]

Substituting x value in any of the two equation we can find corresponding y value .

2x-3y=1

[tex] 2 (\frac{3}{4} ) -3y=1 [/tex]

Solving for y

y= [tex] \frac{1}{6} . [/tex]

The point of intersection of the two lines is ( [tex] (\frac{3}{4} ,\frac{1}{6} ) [/tex]


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