The pair of lines nbsp- nbsp-and 2x - 7y - 5 - 0 are consistent- nbsp-x-3x-1x-2

The correct option is C x=2For a pair of lines to be consistent, either a_1/a_2≠b_1/b_2 or nbsp;a_1/a_2=b_1/b_2=c_1/c_2. In x = 2; 2x 7y 5 = 0, a_1/a_2≠b_ ...

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Byju's Answer

Standard X

Mathematics

Graphical Method of Finding Solution of a Pair of Linear Equations

The pair of l...

Question

The pair of lines and $2 x - 7 y - 5 = 0$ are consistent.

x = 3

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x = 1

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x = 2

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Solution

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

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2 x - 7 y - 5 = 0

are consistent.

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(k - 1) x + (k^{2} - 7) y - 5 = 0

and

(k - 2) x + (2 k - 5) y = 0

are

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The pair of lines and 2x−7y−5=0 are consistent.

The correct option is C x=2For 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. Therefore, the equations x=2 and 2x−7y−5=0 are consistent.

The pair of lines and $2 x - 7 y - 5 = 0$ are consistent.