Which of these pairs of lines are parallel?

y = 3; 2x - 7y - 5 = 0

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3y - 2x = 2; 3x - 2y = 2

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$\sqrt{3} x - y = 2; \sqrt{6} x - \sqrt{2} y = 2$

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$\frac{x}{3} + \frac{y}{2} = 1; x + \frac{3 y}{2} = 3$

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Solution

The correct option is C
$\sqrt{3} x - y = 2; \sqrt{6} x - \sqrt{2} y = 2$

Write the two equations in the general form where
$a_{1} x + b_{1} y + c_{1} = 0 a n d$
$a_{2} x + b_{2} y + c_{2} = 0$ ,
For two lines to be parallel, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} For \sqrt{3 x} - y = 2; \sqrt{6 x} - \sqrt{2} y = 2, \frac{a_{1}}{a_{2}} = \frac{\sqrt{3}}{\sqrt{6}} = \frac{1}{\sqrt{2}} \frac{b_{1}}{b_{2}} = \frac{- 1}{- \sqrt{2}} = \frac{1}{\sqrt{2}} \frac{c_{1}}{c_{2}} = \frac{- 2}{- 2} = 1 Hence \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} .$

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Similar questions

Which of these following equations have $x = - 3, y = 2$ as solutions?

Q. Solve the following pairs of equations by reducing them to a pair of linear equations:

(i)

\frac{1}{2 x} + \frac{1}{3 y} = 2; \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

(ii)

\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1

(iii)

\frac{4}{x} + 3 y = 14; \frac{3}{x} - 4 y = 23

(iv)

\frac{5}{x - 1} + \frac{1}{y - 2} = 2; \frac{6}{x - 1} - \frac{3}{y - 2} = 1

(v)

\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15

(vi)

6 x + 3 y = 6 x y; 2 x + 4 y = 5 x y

(vii)

\frac{10}{x + y} + \frac{2}{x - y} = 4; \frac{15}{x + y} - \frac{5}{x - y} = - 2

(viii)

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}; \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Q. Divide

2 x^{3} y - 6 x^{2} y^{3} + 6 x^{2} y^{2}

2 x^{2} y

Solve the following pair of linear equations by the elimination method and the substitution method :

(i) x+y=5 and 2x−3y=4
(ii) 3x+4y=10 and 2x−2y=2
(iii) 3x−5y−4=0 and 9x=2y+7
(iv) x2+2y3=−1 and x−y3=3

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Which of these pairs of lines are parallel?

The correct option is C √3x−y=2;√6x−√2y=2 Write the two equations in the general form where a1x+b1y+c1=0 and a2x+b2y+c2=0, For two lines to be parallel, a1a2=b1b2≠c1c2For √3x−y=2;√6x−√2y=2,a1a2=√3√6=1√2b1b2=−1−√2=1√2c1c2=−2−2=1Hence a1a2=b1b2≠c1c2.