Write the nature of the lines representing the linear equation $2 x - y = 3$ and $4 x - y = 5$ .

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Solution

$2 x - y = 3$
$4 x - y = 5$
$\frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}$
$\frac{b_{1}}{b_{2}} = \frac{- 1}{- 1} = 1$
$\frac{c_{1}}{c_{2}} = \frac{3}{5}$
Since,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
So, the lines intersect at one point.

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Q. The lines representing the linear equations

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and

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Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

and

\frac{c_{1}}{c_{2}}

find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:

2 x - y = 3; 4 x - y = 5

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
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Determine the vertices of the triangle formed by the lines representing the above equation and the y-axis.

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Write the nature of the lines representing the linear equation 2x−y=3 and 4x−y=5.

2x−y=34x−y=5a1a2=24=12b1b2=−1−1=1c1c2=35Since,a1a2≠b1b2So, the lines intersect at one point.

Write the nature of the lines representing the linear equation $2 x - y = 3$ and $4 x - y = 5$ .

$2 x - y = 3$
$4 x - y = 5$
$\frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}$
$\frac{b_{1}}{b_{2}} = \frac{- 1}{- 1} = 1$
$\frac{c_{1}}{c_{2}} = \frac{3}{5}$
Since,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
So, the lines intersect at one point.