The value of c for which the pair of equation | vedclass

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

Question

(B) The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is $\frac{a_1}{

Vedclass · Accepted Answer

no value

Vedclass · Answer

(B) The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.The given equations are $cx - y - 2 = 0$ and $6x - 2y - 3 = 0$.Here,$a_1 = c, b_1 = -1, c_1 = -2$ and $a_2 = 6, b_2 = -2, c_2 = -3$.Applying the condition: $\frac{c}{6} = \frac{-1}{-2} = \frac{-2}{-3}$.This simplifies to $\frac{c}{6} = \frac{1}{2} = \frac{2}{3}$.Since $\frac{1}{2} 
eq \frac{2}{3}$,there is no value of $c$ that satisfies both equalities simultaneously.Therefore,the pair of equations will have no value of $c$ for which they have infinitely many solutions.

The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 3$ will have infinitely many solutions is

Similar Questions

Draw the graphs of the equations $x=3, x=5$ and $2x-y-4=0$. Also,find the area of the quadrilateral formed by these lines and the $x$-axis.

Find the solution of the pair of equations $\frac{x}{10} + \frac{y}{5} - 1 = 0$ and $\frac{x}{8} + \frac{y}{6} = 15$. Hence,find $\lambda$ if $y = \lambda x + 5$.

The solution of the pair of equations $x+y-1=0$ and $2x+2y-3=0$ is:

Draw the graphs of the equations $2x + 3y = 8$ and $x + 2y = 5$ on the same graph paper. Find the solution of the system from the graph.

Determine,algebraically,the vertices of the triangle formed by the lines:
$3x - y = 3$
$2x - 3y = 2$
$x + 2y = 8$

Vedclass Test Series

Exam Paper Generator

Online Exam Module