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How to Solve Parallel and Perpendicular Lines?

TopLines have a straight Geometry and so they can either be parallel or intersecting. Two equations are said to be perpendicular if product of their respective slopes is equals to -1. Being perpendicular, these lines are intersecting too. As we know that two Linear Equations can intersect at just one Point, same is true for two Perpendicular Lines also. Two lines are said to be parallel if they are having same Slope, considered vertically or horizontally. Solution of two Parallel Lines can - not be found because they do not intersect each other but for perpendicular lines we have a solution. Solution for two perpendicular lines can be found by solving linear equations in usual way. Let us learn how to solve parallel and perpendicular lines?

Suppose there are two lines: 5 a + 4 b = 10 and 5 a + 4b = 20. On evaluating slopes of two lines we get:
b = -5a/4 + 5/2 and b = -5a/4 + 5,

Thus, m1 = -5/2 and m2 = -5. We see that two lines have slopes and so they do not intersect each other. But in case of lines given as: 5a + 4b = 10 and 5a - 4b = 20 we see that two slopes differ and also their product is -1 so they are perpendicular too. So, we conclude that two lines have an Intersection point. To solve these lines we add two lines as follows:

(5 a + 4 b = 10) + (5 a - 4 b = 20) = (10a = 30) or a = 3,
Thus there intersection point is: (3, -5/4).