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

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

Q. Question 1(ii)
Do the following pair of linear equations have no solution? Justify your answer.
x = 2y and y = 2x

Q. Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22

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.
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Role of Coefficients and Constants

Standard IX 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