Determine whether or not the four straight lines with equations x + 2y – 3 = 0,
3x + 4y - 7 = 0, 2x + 3y - 4= 0 and 4x + 5y - 6= 0 are concurrent.
Answers
Given : x + 2y – 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4= 0 and 4x + 5y - 6= 0
To find : whether or not the four straight lines are concurrent.
Solution:
Lines will be concurrent if they all meet at one point
x + 2y – 3 = 0 Eq1
3x + 4y - 7 = 0, Eq2
2x + 3y - 4= 0 Eq3
4x + 5y - 6= 0 Eq4
Solving Eq 1 & Eq2
3 * Eq1 - Eq 2
=> 3x + 6y - 9 - (3x + 4y - 7) = 0
=> 2y - 2 =0
=> y = 1
x + 2 - 3 = 0
=> x = 1
( 1 , 1) is the intersection point of 1st two lines
Lets check other two line goes through that point or not
2x + 3y - 4= 0
=> 2(1) + 3(1) - 4 = 0
=> 1 = 0
but 1 ≠ 0
Hence 2x + 3y - 4= 0 line does not go through ( 1 , 1)
4x + 5y - 6= 0
=> 4 + 5 - 6 = 0
=> 3 = 0
but 3 ≠ 0
Hence 4x + 5y - 6= 0 line does not go through ( 1 , 1)
four straight lines are not concurrent.
Learn more:
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