Question

For what value of k does the pair of equations kx - y =2 and 6x -2y =4 have infinietly many solutoins?​

Answer 1

Answer:

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Answer 2

Topic :-

Linear equations in two variables

Given :-

Equations are, kx - y = 2 and 6x - 2y = 4

To find :-

Value of k for which the equation has infinitely many solutions.

Solution :-

Firstly before solving the problem, we should know about the solutions of pair of equations. The point where both the linear equations cross or intersect each other is called the solution of equation.

For the given equation to have infinity many solutions or we can say that for the given equation to intersect each other infinitely times, there is only one condition, i.e. when both the lines are coincident lines. In simple words, two lines are said to be coincident, when both the lines lies on each other.

The general form of any linear equation in two variable is :

• ax + by + c = 0

The case when two lines are coincident is when the value of :

• a1 / a2 = b1 / b2 = c1 / c2

Here a1, b1 and c1 are the coefficient of x, coefficient of y and constant terms of a general form of linear equation whereas a2, b2 and c2 are that of other equation.

In the given equation 1 :

• a1 = k
• b1 = - 1
• c1 = - 2

In the given equation 2 :

• a2 = 6
• b2 = - 2
• c2 = - 4

Now we get,

→ a1 / a2 = b1 / b2 = c1 / c2

→ k / 6 = - 1 / -2 = -2 / -4

→ k / 6 = 1 / 2 = 1 / 2

→ k / 6 = 1 / 2

→ k = 6 / 2

→ k = 3

So the value of k must be equals to 3 for the given equation to have infinitely many solutions.

Hence required value of k is 3.