check the given equations have either unique solution or infinite solution or no solution. 5x-3y=8,10x-6y=19

Question

check the given equations have either unique solution or infinite solution or no solution. 5x-3y=8,10x-6y=19​

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Sadie 2 months 2021-07-27T22:30:29+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-27T22:31:55+00:00

    No solution

    \\

    Explanation:

    In the given pair of linear equations,

    For first Equation:

    • a₁ = 5
    • b₁ = -3
    • c₁ = 8

    \\

    For the second Equation:

    • a₂ = 10
    • b₂ = -6
    • c₂ = 19

    \\

    For finding whether the equations have unique solution, infinitely many solutions or no solution let’s compare the ratios.

    Here,

     \tt{\dfrac{5}{10}  =  \dfrac{ - 3}{ - 6}  \neq \dfrac{8}{19}} \\  \\

     \implies \tt{ \dfrac{1}{2} =  \dfrac{1}{2}  \neq \dfrac{8}{19}  } \\  \\

     \tt{ \dfrac{a _{1} }{a _{2}}  =  \dfrac{b_{1} }{b _{2} }  \neq \dfrac{c _{1} }{c _{2} }}  \\  \\

    So, the given pair of linear equations does not have any solution.

    KNOW MORE:

    • If a1/a2 = b1/b2 = c1/c2, then the given pair of linear equations would have infinitely many solutions.
    • If a1/a2 ≠ b1/b2 ≠ c1/c2, then the given pair of linear equations would have unique solution.

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