The lines representing the linear equations $2 x - y - 3$ and $4 x - y = 5$

intersect at a point

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

are parallel

No worries! We‘ve got your back. Try BYJU‘S free classes today!

are coindicent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

intersect at exactly two points

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A intersect at a point
The given lines are
$2 x - y = 3$
Here $a_{1} = 2, b_{1} = - 1, c_{1} = 3$
and $4 x - y = 5$
Here $a_{2} = 4, b_{2} = - 1, c_{2} = 5$
$∴ \frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2}$ and $\frac{b_{1}}{b_{2}} = 1$
$∵ \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Thus, lines will intersect at a point. Hence the correct option is (A).

Suggest Corrections

Similar questions

Q. The graphs

y = 2 x^{3} - 4 x + 2

and

y = x^{3} + 2 x - 1

intersect at exactly 3 distinct points. The slope of the line passing through two of these points

Q. The graphs

y = 2 x^{3} - 4 x + 2

and

y = x^{3} + 2 x - 1

intersect at exactly three distinct points. The slope of the line passing through two of these points

Question 1
Graphically, the pair of equations
6x – 3y + 10 = 0
x – y + 9 = 0
Represents two lines which are
(A) intersecting at exactly one point.
(B) intersecting at exactly two points.
(C) coincident.
(D) parallel.

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

Q. Write the nature of the lines representing the linear equation

2 x - y = 3

and

4 x - y = 5

Join BYJU'S Learning Program

The lines representing the linear equations 2x−y−3 and 4x−y=5

The correct option is A intersect at a pointThe given lines are2x−y=3Here a1=2,b1=−1,c1=3and 4x−y=5Here a2=4,b2=−1,c2=5∴a1a2=24=12 and b1b2=1∵a1a2≠b1b2Thus, lines will intersect at a point. Hence the correct option is (A).

The lines representing the linear equations $2 x - y - 3$ and $4 x - y = 5$