Question

The pair of linear equations 76x + ky+ k ,14x+2y =k+1 has infintiely many solutions if the value of k is = answers

Answer 1

The equation are

2x+ky−k=0

4x+2y−(k+1)=0

Here,

$a </p><p>1</p><p> </p><p> =2,b </p><p>1</p><p> </p><p> =k,c </p><p>1</p><p> </p><p> =−k$

and

$a2</p><p> </p><p> =4,b </p><p>2</p><p> </p><p> =2,c </p><p>2</p><p> </p><p> =−(k+1)$

For the system to have infinite solutions,

$a1 \div a2=b1 \div b2=c2c1</p><p> \\ ⇒42=2k \\ =−(k+1)−k</p><p></p><p></p><p>$

Taking,

2/4=k/2

⇒4k=4

⇒k=1

Taking,

k/2= −k/−(k+1)

⇒k+1=2

⇒k=1

So, k=1 is the answer

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