Find the value of k for the following pair of | vedclass

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

Question

(B) For a system of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have no solution,the condition is $\frac{a_1}{a_2} = \frac

Vedclass · Accepted Answer

$-\frac{4}{3}$

Vedclass · Answer

(B) For a system of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have no solution,the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$.Given equations are $2x - ky + 3 = 0$ and $3x + 2y - 1 = 0$.Here,$a_1 = 2, b_1 = -k, c_1 = 3$ and $a_2 = 3, b_2 = 2, c_2 = -1$.Applying the condition $\frac{a_1}{a_2} = \frac{b_1}{b_2}$:$\frac{2}{3} = \frac{-k}{2}$Multiplying both sides by $2$,we get $4 = -3k$.Therefore,$k = -\frac{4}{3}$.Checking the condition $\frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$:$\frac{-(-4/3)}{2} = \frac{4/3}{2} = \frac{2}{3}$.Since $\frac{c_1}{c_2} = \frac{3}{-1} = -3$,and $\frac{2}{3} 
eq -3$,the condition holds true for $k = -\frac{4}{3}$.

Find the value of $k$ for the following pair of linear equations such that the system has no solution:
$2x - ky + 3 = 0$
$3x + 2y - 1 = 0$

Similar Questions

Solve the following pairs of equations by cross-multiplication method:
$3x + y = 5$
$5x + 3y = 3$

If $2x + 3y = 7$ and $3x + 2y = 3$,then the value of $x + y$ is ..........

For what value of $k,$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?

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

In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Find the value of $k$ for the following pair of linear equations such that the system has no solution:$2x - ky + 3 = 0$$3x + 2y - 1 = 0$