(A) Given equations are:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x +

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

(A) Given equations are:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,we obtain:$a_{1} = 5, b_{1} = -4, c_{1} = 8$$a_{2} = 7, b_{2} = 6, c_{2} = -9$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{5}{7}$$\frac{b_{1}}{b_{2}} = \frac{-4}{6} = -\frac{2}{3}$Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$,the lines representing the given pair of linear equations intersect at exactly one point.

Class 10 Mathematics Pair of Linear Equations in Two Variables Textbook - Pair of Linear Equations in Two Variables

Easy

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 are coincident:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$

A
Intersect at a point
B
Parallel
C
Coincident
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Pair of Linear Equations in Two Variables

Subtopic

Textbook - Pair of Linear Equations in Two Variables

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

Difficult

View Solution

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{10}{x+y} + \frac{2}{x-y} = 4$
$\frac{15}{x+y} - \frac{5}{x-y} = -2$

Difficult

View Solution

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

Easy

View Solution

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.
$2x - 3y = 8$; $4x - 6y = 9$

Easy

View Solution

In a $\Delta ABC$,$\angle C = 3 \angle B = 2(\angle A + \angle B)$. Find the three angles.

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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 are coincident:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$

Similar Questions

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

Solve the following pairs of equations by reducing them to a pair of linear equations:$\frac{10}{x+y} + \frac{2}{x-y} = 4$$\frac{15}{x+y} - \frac{5}{x-y} = -2$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.$2x - 3y = 8$; $4x - 6y = 9$

In a $\Delta ABC$,$\angle C = 3 \angle B = 2(\angle A + \angle B)$. Find the three angles.

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 are coincident:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{10}{x+y} + \frac{2}{x-y} = 4$
$\frac{15}{x+y} - \frac{5}{x-y} = -2$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.
$2x - 3y = 8$; $4x - 6y = 9$