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

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1. No solution

   [tex]\\[/tex]

   Explanation:

   In the given pair of linear equations,

   For first Equation:

   • a₁ = 5
   • b₁ = -3
   • c₁ = 8

   [tex]\\[/tex]

   For the second Equation:

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

   [tex]\\[/tex]

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

   Here,

   [tex] \tt{\dfrac{5}{10} = \dfrac{ – 3}{ – 6} \neq \dfrac{8}{19}} \\ \\ [/tex]

   [tex] \implies \tt{ \dfrac{1}{2} = \dfrac{1}{2} \neq \dfrac{8}{19} } \\ \\ [/tex]

   [tex] \tt{ \dfrac{a _{1} }{a _{2}} = \dfrac{b_{1} }{b _{2} } \neq \dfrac{c _{1} }{c _{2} }} \\ \\ [/tex]

   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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