Question

The pair of linear equations x – 2y = 5 and 2x – 4y = 10 have :
(a) Many Solutions
(b) No Solution
(c) One Solution
(d)Two Solution

Answer 1

(c) One Solution

IS THE RIGHT ANSWER
BECAUSE LINEAR EQUATIONS HAVE ONLY ONE SOLUTION.

Answer 2

Answer:

The pair of linear equations x – 2y = 5 and 2x – 4y = 1 have No Solution.

Step-by-step explanation:

Given :

The pair of equations $x - 2y = 5$ and $2x -4y = 1$

To find :

The pair of linear equations have:

(a) Many Solutions

(b) No Solution

(c) One Solution

(d)Two Solution

Step 1

Write down the given pair of equations

Here the given pair of linear equations are

$x - 2y = 5 - - - - (1)$

$2x - 4y = 1 - - - - (2)$

Step 2

Comparing the above linear equations with

a₁ x + b₁ y = c₁ and a₂ x + b₂ y = c₂ we get

$a_{1} = 1 , b_{1} = - 2 , c_{1} = 5$ and

$a_{2} =2 , b_{2} = - 4 , c_{2} = 1$

Step 3

Now we have,

$\frac{a_{1}}{a_{2}}=\frac{1}{2}$

$\frac{b_{1}}{b_{2}}=\frac{-2}{-4}=\frac{1}{2}$

$\frac{c_{1}}{c_{2}}=\frac{5}{1}=5$

Thus we get,

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\neq \frac{c_{1}}{c_{2}}$

So the pair of linear equations $x - 2y = 5$ and $2x - 4y = 1$ have no Solution

Therefore, the correct answer is option (b) No Solution.

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