Question

Determine th value of k if has a unique Solution (K+1)x+5y=4;3x+5y=7

Answer 1

(K+1)x+5y=4 and 3x+5y=7 have unique solution.

a₁ = k+1 ; b₁ = 5 ; c = -4
a₂ = 3 ; b₂ = 5 ; c = -7


Two linear equations has unique solution if $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$\frac{k+1}{3} \neq \frac{5}{5} \\ \\ \frac{k+1}{3} \neq 1 \\ \\ k+1 \neq 3 \\ \\ k \neq 3-1 \\ \\ k \neq 2$

[tex]The value of k is not equal to 2,then the equations have unique solution.

So,any other value of k except 2 is satisfied with the given condition.
∴ The value of k can be any real number but not 2. (k ≠ 2)