If the following pair of equations has infini | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given equations are:$5x + 2y - k = 0$  .......... $(1)$$10x + 4y - 3 = 0$ .......... $(2)$Comparing these with the general form $a_1x + b_1y +

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(B) The given equations are:$5x + 2y - k = 0$  .......... $(1)$$10x + 4y - 3 = 0$ .......... $(2)$Comparing these with the general form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:$a_1 = 5, b_1 = 2, c_1 = -k$$a_2 = 10, b_2 = 4, c_2 = -3$For a pair of linear equations to have infinite solutions,the condition is:$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$Substituting the values:$\frac{5}{10} = \frac{2}{4} = \frac{-k}{-3}$$\frac{1}{2} = \frac{1}{2} = \frac{k}{3}$Taking the equality $\frac{1}{2} = \frac{k}{3}$,we get:$k = \frac{3}{2}$Thus,for $k = \frac{3}{2}$,the system has infinite solutions.

If the following pair of equations has infinite solutions,then find the value of $k$:
$5x + 2y = k$
$10x + 4y = 3$

Similar Questions

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} = -1 - \frac{3}{b}$
$\frac{9}{b} = \frac{4}{a} + 7$

The sum of the digits of a two-digit number is $9$. If $27$ is added to it,the digits of the number get reversed. The number is

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

Four years ago,the sum of the ages of four persons was $40$ years. After two years,the sum of the ages of the same four persons will be ............ years.

Solve the following pair of linear equations by the method of elimination:
$4x - 3y = 8$
$6x - y = \frac{29}{3}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If the following pair of equations has infinite solutions,then find the value of $k$:$5x + 2y = k$$10x + 4y = 3$