Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

Open in App

Solution

$3 x + y - 3 = 0 a n d 2 x + \frac{2}{3} y - 2 = 0 H e r e, a_{1} = 3, b_{1} = 1, c_{1} = - 3 a_{2} = 2, b_{2} = 2 / 3, c_{1} = - 2 \frac{a_{1}}{a_{2}} = \frac{3}{2} a n d \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{3}{2} \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Hence, the given pair of linear equations is coincident and having infinitely many solutions.

Suggest Corrections

Similar questions

Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

Question 1 (i)
Do the following pair of linear equations have no solution? Justify your answer.
2x + 4y = 3 and 12y + 6x = 6

Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3 x + \frac{1}{7} y = 3 a n d 7 x + 3 y = 7$

The following pair of linear equations have one solution

3 x + 3 y = 0

2 x + \frac{2}{3} y = 2

Question 3 (ii)
Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2} a n d \frac{1}{5} x - 3 y = \frac{1}{6}$

Join BYJU'S Learning Program

Question 1(iii) Do the following pair of linear equations have no solution? Justify your answer. 3x + y – 3 = 0 and 2x + 23 y = 2

3x+y−3=0 and 2x+23 y−2=0Here, a1=3, b1=1, c1=−3a2=2, b2=2/3, c1=−2a1a2=32 and b1b2=c1c2=32a1a2=b1b2=c1c2 Hence, the given pair of linear equations is coincident and having infinitely many solutions.

Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2