Question

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

Answer 1

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.