# At what point do the lines 2x +3y =5 and x=2 intersect in (x,y) plane ?

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### 1 Answer

Currently, the evaluation of the point of intersection of two lines ,whose equations are given, is made solving the following system of equations, such that:

`{(2x + 3y = 5),(x = 2):}`

Replacing 2 for x in the top equation yields:

`2*2 + 3y = 5 => 3y = 5 - 4 => 3y = 1 => y = 1/3`

Hence, evaluating the point of intersection of the given lines, yields `(2,1/3).`

You may sketch these two lines to test if they intersect to `(2,1/3)` , such that:

You should notice that the vertical line `x = 2` intersects the red line `2x + 3y = 5` at `y = 1/3` (below the horizontal line `y = 1` ).

**Hence, evaluating the point `(x,y)` where the given lines intersect, yields `(2,1/3)` .**