# For what value of k will the system of linear equations 2x+ky=1 ; 3x-5y=7 has a unique solution..

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the given system of linear equations are of the form

2x+ky=1 a₁x +b₁y+c₁ = 0

3x-5y=7 a₂x +b₂y+c₂ = 0

the condition for unique solution is a₁/a₂≠ b₁b₂

here ,

a₁ = 2, a₂ = 3

b₁ = k ,b₂ = -5

⇒ 2/3 ≠k/ -5

⇒-10 ≠ 3k

⇒k ≠ -10/3

therefore , the value of

2x + ky = 1

3x - 5y = 7

For the system of equations to have a unique solution,

a₁/a₂ ≠ b₁/b₂

∴2/3 ≠ k/-5

∴2/3 ≠ -k/5

∴2/3 * 5 ≠ -k

∴10/3 ≠ - k

∴

Thus, k can be any real value except -10/3.

Thus, k ∈ R - {-10/3}