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WORKBOOK
A) Intersecting Lines:
If a b , then the lines and are intersecting at a point which is called intersection point of
d e
and .
That is, the system of equations ++ = ++ = has a unique solution
Ex: Are the following pairs of lines intersecting? If so, find the coordinates of intersection
point.
a) x+y = 0 x−y = 4 b) x= 3 x−2y = 5 c) 3x+2y = 1
2x−3y = −2
Ex: For which value of k , the following system equation does not have a unique solution ?
(k−2)x+3y = 1 3x−y = 7
B) Parallel Lines :
If a b c , then the lines and are parallel ( // ) ,
d e f
which means that and are NOT intersecting.
If // , the system of equations ax+by+c = 0 dx+ey+f = 0 has no
solution.
Note that, two lines are parallel If and only If their slopes are equal.
That is , // ⇔ = .
This means that, any two nonvertical parallel lines have equal slopes.
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