Question

किसी रैखिक समीकरण युग्म a1x +b1y + c1 =0,a2x +b2y +c2=0 के एक अद्वितीय हल तथा अनंत्ता अनेक हल होने के लिए प्रतिबंध लिखिए ​

Answer 1

Step-by-step explanation:

Let's solve for a.

a1x+b1y+c1=0

Step 1: Add -by to both sides.

ax+by+c+−by=0+−by

ax+c=−by

Step 2: Add -c to both sides.

ax+c+−c=−by+−c

ax=−by−c

Step 3: Divide both sides by x.

ax/x=−by−c/x

a=−by−c/x

Answer:

a=−by−c/x

Answer 2

SOLUTION

TO DETERMINE

The condition for unique solution and infinite number of solutions for two linear equations

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

EVALUATION

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions :

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}$

Inconsistent :

No solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

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