For what value(s) of k does the pair of equat | vedclass

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

Question

(D) The given pair of linear equations is:$kx + 3y = (k - 3)$$12x + ky = k$Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:$

Vedclass · Accepted Answer

$-6$

Vedclass · Answer

(D) The given pair of linear equations is:$kx + 3y = (k - 3)$$12x + ky = k$Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:$a_1 = k, b_1 = 3, c_1 = -(k - 3)$$a_2 = 12, b_2 = k, c_2 = -k$For the pair of linear equations to have no solution,the condition is:$\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$$\frac{k}{12} = \frac{3}{k} 
eq \frac{-(k - 3)}{-k}$Taking the first two parts:$\frac{k}{12} = \frac{3}{k} \Rightarrow k^2 = 36 \Rightarrow k = \pm 6$Now,checking the condition $\frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$:If $k = 6$,then $\frac{3}{6} = \frac{1}{2}$ and $\frac{k-3}{k} = \frac{6-3}{6} = \frac{3}{6} = \frac{1}{2}$. Since $\frac{1}{2} = \frac{1}{2}$,$k = 6$ gives infinitely many solutions.If $k = -6$,then $\frac{3}{-6} = -\frac{1}{2}$ and $\frac{k-3}{k} = \frac{-6-3}{-6} = \frac{-9}{-6} = \frac{3}{2}$. Since $-\frac{1}{2} 
eq \frac{3}{2}$,the condition holds.Thus,the value of $k$ for which there is no solution is $-6$.

For what value$(s)$ of $k$ does the pair of equations $kx + 3y = k - 3$ and $12x + ky = k$ have no solution?

Similar Questions

The solution set of $x+y-1=0$ and $3x+3y-2=0$ is ...........

Solve the following pair of equations: $2x + y = \frac{7xy}{3}, x + 3y = \frac{11xy}{3}$

Half the perimeter of a rectangular garden,whose length is $4 \, m$ more than its width,is $36 \, m$. Represent this as a pair of linear equations in two variables.

Solve the following pairs of linear equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{xy}, \quad \frac{4}{x} + \frac{9}{y} = \frac{21}{xy} \quad (x \neq 0, y \neq 0)$

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module