
The graphs of $2x + 3y - 6 = 0,4x - 3y - 6 = 0{\text{ ,}}x = 2{\text{ and }}y = \dfrac{2}{3}$ intersect in
A.Four points
B.One point
C.In no points
D.Infinite number of points
Answer
591.9k+ views
Hint: In order to solve this question we need to find the point of intersection of these lines. We will find the point of intersection of the first two lines and then the third line with others.
Complete step-by-step answer:
Given
\[
2x + 3y - 6 = 0......................(1) \\
4x - 3y - 6 = 0......................(2) \\
x = 2......................................(3) \\
y = \dfrac{2}{3}....................................(4) \\
\]
Adding and solving equation (1) and (2) we get
\[
\Rightarrow2x + 3y - 6 + 4x - 3y - 6 = 0 \\
\Rightarrow 6x = 12 \\
\Rightarrow x = 2 \\
\]
Substituting the value of x in equation (1), we get
\[
\Rightarrow 2 \times 2 + 3y - 6 = 0 \\
\Rightarrow 3y = 2 \\
\Rightarrow y = \dfrac{2}{3} \\
\]
Hence the point of intersection of these two lines is $\left( {2,\dfrac{2}{3}} \right)$
Also $x = 2$ and $ y = \dfrac{2}{3}$ passes through the same point of intersection $\left( {2,\dfrac{2}{3}} \right)$ .
Hence, all passes through only one point of intersection.
So, option B is the correct option.
Note: In order to solve these types of questions, remember the basic concept of solving the equations such as elimination method, cross multiplication method and substitution method. Also remember the concept of slope and equations of straight lines. There are five equations of straight lines such as slope intercept form. These types of problems can also be solved by the method of graphs, but it is rather more simpler by the method of algebra.
Complete step-by-step answer:
Given
\[
2x + 3y - 6 = 0......................(1) \\
4x - 3y - 6 = 0......................(2) \\
x = 2......................................(3) \\
y = \dfrac{2}{3}....................................(4) \\
\]
Adding and solving equation (1) and (2) we get
\[
\Rightarrow2x + 3y - 6 + 4x - 3y - 6 = 0 \\
\Rightarrow 6x = 12 \\
\Rightarrow x = 2 \\
\]
Substituting the value of x in equation (1), we get
\[
\Rightarrow 2 \times 2 + 3y - 6 = 0 \\
\Rightarrow 3y = 2 \\
\Rightarrow y = \dfrac{2}{3} \\
\]
Hence the point of intersection of these two lines is $\left( {2,\dfrac{2}{3}} \right)$
Also $x = 2$ and $ y = \dfrac{2}{3}$ passes through the same point of intersection $\left( {2,\dfrac{2}{3}} \right)$ .
Hence, all passes through only one point of intersection.
So, option B is the correct option.
Note: In order to solve these types of questions, remember the basic concept of solving the equations such as elimination method, cross multiplication method and substitution method. Also remember the concept of slope and equations of straight lines. There are five equations of straight lines such as slope intercept form. These types of problems can also be solved by the method of graphs, but it is rather more simpler by the method of algebra.
Recently Updated Pages
Master Class 11 Chemistry: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

How many 5 digit telephone numbers can be constructed class 11 maths CBSE

Draw a well labelled diagram of reflex arc and explain class 11 biology CBSE

What is the difference between noise and music Can class 11 physics CBSE

Trending doubts
In what year Guru Nanak Dev ji was born A15 April 1469 class 11 social science CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

10 examples of friction in our daily life

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

