Question

*x+y=6 and 2x+2y=12 then these equations have ............*

1️⃣ no solution
2️⃣ infinite solutions
3️⃣ only one solution
4️⃣ none of these​

Answer 1

Answer:

infinite solutions

Step-by-step explanation:

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Answer 2

Answer:

The given simultaneous equations have infinite solutions.

Option ( 2 )

Step-by-step-explanation:

The given simultaneous equations are

x + y = 6 and 2x + 2y = 12.

Now,

x + y = 6 - - ( 1 )

Comparing with ax + by + c = 0, we get,

• a₁ = 1
• b₁ = 1
• c₁ = 6

Now,

2x + 2y = 12 - - ( 2 )

Comparing with ax + by + c = 0, we get,

• a₂ = 2
• b₂ = 2
• c₂ = 12

Now,

$\displaystyle{\sf\:\dfrac{a_1}{a_2}\:=\:\dfrac{1}{2}\:\:\:-\:-\:(\:3\:)}$

Now,

$\displaystyle{\sf\:\dfrac{b_1}{b_2}\:=\:\dfrac{1}{2}\:\:\:-\:-\:(\:4\:)}$

Now,

$\displaystyle{\sf\:\dfrac{c_1}{c_2}\:=\:\cancel{\dfrac{6}{12}}}$

$\displaystyle{\implies\sf\:\dfrac{c_1}{c_2}\:=\:\dfrac{1}{2}\:\:\:-\:-\:-\:(\:5\:)}$

From equations ( 3 ), ( 4 ) & ( 5 ),

$\displaystyle{\underline{\boxed{\red{\sf\:\dfrac{a_1}{a_2}\:=\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}}}}}$

∴ The given simultaneous equations have infinite solutions.