Question

The pair of equations x+ 2y+5=0 and -3x-6y-10=0 have

Answer 1

AnsWer :

D) No Solution.

Correct QuestioN :

The pair of equations x + 2y + 5 = 0 and - 3x - 6y - 10 = 0 have,

• A) A unique solution.
• B) Exactly two solutions.
• C) Infinitely many solutions.
• D) No solutions.

SolutioN :

Let,

• x + 2y + 5 = 0.
• - 3x - 6y - 10 = 0.

☛ Many Solution.

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{a_2}= \dfrac{b_1}{b_2}= \dfrac{c_1}{c_2}$

Where as,

• a1 = 1.
• a2 = - 3.
• b1 = 2.
• b2 = - 6.
• c1 = 5.
• c2 = - 10.

$\tt \dagger \: \: \: \: \: - \dfrac{1}{3}= - \dfrac{2}{6}= - \dfrac{5}{10}$

$\tt : \implies \dfrac{1}{3}= \dfrac{1}{3}= \dfrac{1}{2}$

✎ We are notice,

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{a_2}= \dfrac{b_1}{b_2} \red{ \neq \dfrac{c_1}{c_2} }$

✡ So, Condition not satisfied.

$\rule{200}2$

☛ Unique Solution.

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$

$\tt : \implies - \dfrac{1}{3} \neq - \dfrac{2}{6}$

$\tt : \implies \dfrac{1}{3} \neq \dfrac{1}{3}$

✎ We are notice,

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{a_2} \red{\neq \dfrac{b_1}{b_2}}$

✡ So, Condition not satisfied.

$\rule{200}2$

☛ No Solution.

$\tt \dagger \: \: \: \: \: \dfrac{a_1}{a_2}= \dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

$\tt : \implies - \dfrac{1}{3}= - \dfrac{2}{6} - \neq - \dfrac{5}{10}$

$\tt : \implies \dfrac{1}{3}= \dfrac{1}{3} \neq \dfrac{1}{2}$

✎ We are notice,

$\tt \dagger \: \: \: \: \: \green{\dfrac{a_1}{a_2}= \dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2} }$

✡ Condition should be satisfied.

Therefore, the given pair of linear equation have, No Solution.

Answer 2

Here is your answer user.