Question

If the given pair of equations has infinitely many solutions, then find the value of $\text{k}$?

$\text{2x + 4y = k}$
$\text{6x + 12y = 9}$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Given,
$\text{6x + 12y = 9}$
$\text{2x + 4y = k}$

A system of equations is said to have infinitely many solutions if both the equations passes through same points.

In the equation, $\text{6x + 12y = 9}$

When $\text{x = 0}\text{12y = 9}\Rightarrow \text{y}=\frac{9}{12}$
$=\frac{3}{4}$------(1)

In the equation, $\text{2x + 4y = k}$

When $\text{x = 0,}$
$\text{4y = k}$
$\Rightarrow \text{y}=\frac{k}{4}$ -------(2)

As we know, both equations pass through the same points, their value of y-coordinate at x-coordinate are equal. Hence, Equation (1) = Equation (2)

$\Rightarrow \frac{k}{4}=\frac{3}{4}$
$\therefore \text{k = 3}$