3x + 2y = 6 and 6x-4y= 9 are parallel lines ? explain
Answers
Answer:
The lines are not parallel they will intersect each other and form a unique solution. For intersecting the condition is: a1/a2 ≠ b1/b2. Hence these lines will intersect and not be parallel. This equation does not satisfy the condition that a1/a2 = b1/b2 ≠ c1/c2.
Step-by-step explanation:
Given Equations:
3x + 2y = 6
6x - 4y = 9
Here,
a1 = 3 a2 = 2 b1 = 2 b2 = - 4 c1 = 6 c2 = 9
For parallel lines,
a1/a2 = b1/b2 ≠ c1/c2
In this equation we will substitute the values we just found out a while ago,
3/6 = 2/-4 = 6/9
Simplifying,
1/2 ≠ -1/2
The lines are not parallel they will intersect each other and form a unique solution. For intersecting the condition is: a1/a2 ≠ b1/b2. Hence these lines will intersect and not be parallel. This equation does not satisfy the condition that a1/a2 = b1/b2 ≠ c1/c2.