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
For x = 3 and y = -1
2x + 3y = 3
⇒ 2 × 3 + 3 × -1 = 3
⇒ 6-3 = 3; which is true.
And 6x + 9y - 9 = 0
⇒ 6 × 3 + 9 × -l -9 = 0
⇒ 18 - 9 - 9 = 0; which is true.
∴ x = 3 and y = -1 is a solution of the given system.
For x = -6 and y = 5
2x + 3y = 3
⇒ 2 × -6 + 3 × 5 = 3
⇒ -12 + 15 = 3; which is true.
⇒ 6x + 9y - 9 = 0
⇒ 6 × -6 + 9 x 5 - 9 = 0
⇒ -36 + 45 - 9 = 0; which is true.
∴ x = -6 and y = 5 is also a solution of the given system.
Yes, the given system of simultaneous linear equations has infinite solutions.
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.
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