If a pair of linear equation is given by a1x b1y c1 = 0 and a2x ...
Explanation:
The given pair of linear equations is:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Given that a1/a2 = b1/b2 and a1/a2 is not equal to c1/c2.
Let's assume that a1/a2 = b1/b2 = k (some constant).
Then, we can write a1 = ka2 and b1 = kb2.
Substituting these values in the first equation, we get:
ka2x + kb2y + c1 = 0
Dividing the entire equation by a2 (since a2 cannot be zero), we get:
kx + (kb2/a2)y + c1/a2 = 0
Similarly, for the second equation, we can write:
a2x + b2y + c2 = 0
Dividing the entire equation by a2, we get:
x + (b2/a2)y + c2/a2 = 0
Comparing the two equations, we can see that:
kx + (kb2/a2)y + c1/a2 = x + (b2/a2)y + c2/a2
Simplifying this, we get:
(x coefficient): k - 1 = 0, i.e., k = 1
(y coefficient): kb2/a2 - b2/a2 = 0, i.e., b1 = b2
(c coefficient): c1/a2 - c2/a2 is not equal to zero, i.e., c1 is not equal to c2
Therefore, the given pair of linear equations is consistent.
Hence, the correct answer is (a) True.
If a pair of linear equation is given by a1x b1y c1 = 0 and a2x ...
B) false