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Question
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
x – 3y – 7 = 0
3x – 3y – 15 = 0
Solution
x – 3y – 7 = 0
3x – 3y – 15= 0
`a_1/a_2 = 1/3`
`b_1/b_2 = (-3)/-3 = 1 `
`c_1/c_2 = (-7)/-15 = 7/15`
`a_1/a_2 ≠ b_1/b_2`
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication,
`x/(45-(21)) = y/(-21-(-15)) = 1/(-3-(-9))`
`x/24 = y/-6 = 1/6`
x/24 = 1/6 and y/-6 = 1/6
x = 4 and y = -1
∴ x = 4, y = -1.
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