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 $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} o r \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .
In x = 2; 2x - 7y - 5 = 0, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} .$ In all the other options, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} .$

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Similar questions

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

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}

Q. The equations

λ x - y = 2, 2 x - 3 y = - λ, 3 x - 2 y = - 1

are consistent for

Q. Divide

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

2 x^{2} y

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

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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≠b1b2ora1a2=b1b2=c1c2. In x = 2; 2x - 7y - 5 = 0, a1a2≠b1b2. In all the other options, a1a2=b1b2≠c1c2.