Which of these pairs of lines are consistent?

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

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3y - 2x = 2; 2x - 3y = 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} = 1

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Solution

The correct option is A x = 2; 2x - 7y - 5 = 0
For a pair of lines to be consistent, either $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} or \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .
In x = 2; 2x - 7y - 5 = 0, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} .$ In all the other options, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} .$

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Similar questions

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

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Q. The equations

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Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

x + y = 5, 2 x + 2 y = 10

(ii)

x - y = 8, 3 x - 3 y = 16

(iii)

2 x + y - 6 = 0, 4 x - 2 y - 4 = 0

(iv)

2 x - 2 y - 2 = 0, 4 x - 4 y - 5 = 0

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Which of these pairs of lines are consistent?

The correct option is A x = 2; 2x - 7y - 5 = 0For a pair of lines to be consistent, either a1a2≠b1b2 or a1a2=b1b2=c1c2. In x = 2; 2x - 7y - 5 = 0, a1a2≠b1b2. In all the other options, a1a2=b1b2≠c1c2.