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

Solve the following pair of linear equations:
$ax + by = c$
$bx + ay = 1 + c$

Romila went to a stationery shop and purchased $2$ pencils and $3$ erasers for ₹ $9$. Her friend Sonali saw the new variety of pencils and erasers with Romila,and she also bought $4$ pencils and $6$ erasers of the same kind for ₹ $18$. Represent this situation algebraically and graphically.

Solve the following pair of linear equations by the substitution method.
$0.2 x + 0.3 y = 1.3$
$0.4 x + 0.5 y = 2.3$

$k$ ની કઈ કિંમત માટે નીચે આપેલ સુરેખ સમીકરણોની જોડને કોઈ ઉકેલ નથી?
$3x + y = 1$
$(2k - 1)x + (k - 1)y = 2k + 1$

The ages of two friends Ani and Biju differ by $3\, years.$ Ani's father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by $30\, years.$ Find the ages of Ani and Biju.

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$