Short Answer TypeWrite whether the following pair of linear equations is consistent or not.
x + y = 14
x - y = 4
Find the value of k so that the following system of equations has infinite solutions:
3x - y - 5 = 0; 6x - 2y + k = 0
Given the linear equation 2a + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :
(i) parallel lines
(ii) intersecting lines
(iii) coincident lines.
10x + 5y - (k - 5) = 0
20x + 10y - k = 0.
Here, we have
a1 = 10 b1 = 5 c1 = - (k - 5)
a2 = 20 b2 = 10 c2 = - k
For infinitely many solutions, we have
Hence, the given system of equations has infinitely many solutions, when k = 10.
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