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Inconsistent Pair of Linear Equations

iii Do the fo...

Question

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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