Question

Find the value of k for which the following system of equations has a unique solution:
x+2y=35x+ky+7=0

Answer 1

k ≠ 10.

Step-by-step explanation:

Given:  

x +2y = 3

5x +ky +7 = 0

The system of equations has a unique solution.

a1 = 1, b1 = 2, c1 = -3

a2 = 5, b2 = k, c2 = -7

So  a1/a2 ≠ b1/b2

1/5 ≠ 2/k

Therefore k ≠ 10.

So for all values of k except 10, the system of equations will have a unique solution.

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

As, it is given equations has unique solution.

We know the case of unique solution.

$\Large{\star{\boxed{\rm{\frac{a_{1}} {a_{2}} ≠ \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}}}}}$

Where,

a1 = 1, a2 = 5

b1 = 2, b2 = k

c1 = -3, c2 = 7

________________[Put Values]

$\sf{→\frac{1}{5} ≠ \frac{2}{k} ≠ \frac{-3}{7}} \\ \\ \sf{→\frac{1}{5} ≠ \frac{2}{k}} \\ \\ \sf{→k ≠ \frac{5 \times 2}{1}} \\ \\ \sf{→k ≠ 10} \\ \\ \Large{\star{\boxed{\sf{k ≠ 10 }}}}$