On comparing the ratios frac{a_{1}}{a_{2}}, f | vedclass

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

Question

(B) Given equations are:$6x - 3y + 10 = 0$$2x - y + 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x +

Vedclass · Accepted Answer

Parallel

Vedclass · Answer

(B) Given equations are:$6x - 3y + 10 = 0$$2x - y + 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,we get:$a_{1} = 6, b_{1} = -3, c_{1} = 10$$a_{2} = 2, b_{2} = -1, c_{2} = 9$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{6}{2} = \frac{3}{1} = 3$$\frac{b_{1}}{b_{2}} = \frac{-3}{-1} = \frac{3}{1} = 3$$\frac{c_{1}}{c_{2}} = \frac{10}{9}$Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} 
eq \frac{c_{1}}{c_{2}}$,the lines representing the given pair of equations are parallel to each other. Therefore,these lines will never intersect at any point,and there is no solution for the given pair of equations.

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel or coincident:
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$

Similar Questions

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

The graph of the equation $2x - y = 1$ does not pass through which of the following points?

Which of the following pairs of linear equations are consistent/inconsistent? If consistent,obtain the solution graphically: $2x + y - 6 = 0, 4x - 2y - 4 = 0$.

Draw the graphs of the pair of linear equations $x+y=10$ and $x-y=4$. Determine the coordinates of the vertices of the triangle formed by these linear equations and the $X$-axis.

Graphically,the pair of equations $6x - 3y + 10 = 0$ and $2x - y + 9 = 0$ represents two lines which are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel or coincident:$6x - 3y + 10 = 0$$2x - y + 9 = 0$