Find whether this pair of equations has a unique solution or an infinite number of solutions or no solution: $3x+5y=13$ , $5x+3y=4$ .

Academic Mathematics NCERT Class 10

Problem Statement

Find whether this pair of equations has a unique solution or an infinite number of solutions or no solution: $3x+5y=13$ , $5x+3y=4$ .

Solution

Given: Pair of equations

$3x+5y=13$ ,

$5x+3y=4$ .

To do: To find whether this pair of equations has a unique solution or an infinite number of solutions or no solution.

Solution:

Given equations are:

$3x+5y=13\ or\ 3x+5y-13=0$ ,

$5x+3y=4\ or\ 5x+3y-4=0$

On comparing with General form of a pair of linear equations in two variables

$x$ &

$y$ is:

$a_1x + b_1y + c_1 = 0$ and

$a_2x + b_2y + c_2= 0$

$a_1=3,\ b_1=5,\ c_1=-13$

$a_2= 5,\ b_2=3,\ c_2=-4$

$\frac{a_1}{a_2}= \frac{3}{5},\ \frac{b_1}{b_2}=\frac{5}{3},\ \frac{c_1}{c_2}=\frac{-13}{-4}=\frac{13}{4}$

Here,

$\frac{a_1}{a_2} eq \frac{b_1}{b_2}$

âHence, this pair of equations has unique solution.

Tutorialspoint

Updated on: 10-Oct-2022

63 Views

Kickstart Your Career

Get certified by completing the course

Advertisements