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

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Solution

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

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Similar questions

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.
$\frac{3}{5} x - y = \frac{1}{2} a n d \frac{1}{5} x - 3 y = \frac{1}{6}$

Q. Question 2 (ii)
Do the following equations represent a pair of coincident lines? Justify your answer.
– 2x – 3y = 1 and 6y + 4x = - 2

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Inconsistent Pair of Linear Equations

Standard X Mathematics

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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, c2=−2a1a2=32 and b1b2=c1c2=32a1a2=b1b2=c1c2 Hence, the given pair of linear equations rerpresent coincident lines and thus has 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