Question

for what value k does the system of equations x+2y=3 and 5x+ky=7 have a unique solution

Answer 1

Step-by-step explanation:

given condition is unique solution so x=y=1

5x+ky=7

5+k=7

k=7-5=2

Answer 2

Question :

For what value of k does the system of equation x +2y = 3 and 5x+ky=7. have a unique solution.

AnsWer :

$K\cancel=10.$

Explanation :

When we have unique solution,

$\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \boxed{ \frac{a_1}{a_2} \cancel = \frac{b_ 1}{b_2 } }$

equation,

x+2y=3.

5x+ky=7.

Where as,

$\: \: \: \: \tt a_1= 1 \: \: \:b_1 = 2\: \: \: and \: \: \:c_1 = 3.$

Putting value,

$\leadsto \tt \frac{1}{5} \cancel = \frac{2}{k} \\ \leadsto \tt k \cancel= 10.$

Therefore, the value of k does pair of linear equation be k not equal to 10.

Important points :

~ Unique Solution - Lines are interesting.

~ Many Solution - Lines are Coincidence.

~ No Solution - Lines are parallel.