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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
2x + y = 5
3x + 2y = 8
Solution
2x + y = 5
3x + 2y = 8
`a_1/a_2=2/3, b_1/b_2=1/2, c_1/c_2=(-5)/-8`
`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 method,
`x/(b_1c_2-b_2c_1) = y/(c_1a_2-c_2a_1)= 1/(a_1b_2-a_2b_1)`
`x/(-8-(-10))=y/(-15+16)=1/(4-3)`
`x/2=y/1=1`
x/2=1, y/1=1
x=2, y = 1
∴ x =2, y =1
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