JEE Exam > JEE Questions > The equations x + 2y + 2z = 1 and 2x + 4 y + ... Start Learning for Free
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have
- a)infinite solution
- b)only one solution
- c)only two solutions
- d)no solution
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite sol...
Community Answer
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite sol...
Solution:
Given equations are:
x + 2y + 2z = 1 …(i)
2x + 4y + 4z = 9 …(ii)
To check whether they have a solution or not, let’s try to solve them.
(ii) can be simplified as follows:
2x + 4y + 4z = 9
=> x + 2y + 2z = 4.5 …(iii)
Now, (i) and (iii) can be written as a matrix equation:
\begin{bmatrix}1&2&2\\1&2&2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix} = \begin{bmatrix}1\\4.5\end{bmatrix}
The coefficient matrix [A] = \begin{bmatrix}1&2&2\\1&2&2\end{bmatrix] has rank 1 as its two rows are proportional to each other. Also, the augmented matrix [A|B] = \begin{bmatrix}1&2&2&1\\1&2&2&4.5\end{bmatrix] has rank 2. Therefore, the system of equations has no solution.
Hence, the correct option is (d) no solution.
Given equations are:
x + 2y + 2z = 1 …(i)
2x + 4y + 4z = 9 …(ii)
To check whether they have a solution or not, let’s try to solve them.
(ii) can be simplified as follows:
2x + 4y + 4z = 9
=> x + 2y + 2z = 4.5 …(iii)
Now, (i) and (iii) can be written as a matrix equation:
\begin{bmatrix}1&2&2\\1&2&2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix} = \begin{bmatrix}1\\4.5\end{bmatrix}
The coefficient matrix [A] = \begin{bmatrix}1&2&2\\1&2&2\end{bmatrix] has rank 1 as its two rows are proportional to each other. Also, the augmented matrix [A|B] = \begin{bmatrix}1&2&2&1\\1&2&2&4.5\end{bmatrix] has rank 2. Therefore, the system of equations has no solution.
Hence, the correct option is (d) no solution.
 | Explore Courses for JEE exam |  |
Top Courses for JEEView all
Top Courses for JEE
Question Description
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer?.
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 havea)infinite solutionb)only one solutionc)only two solutionsd)no solutionCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
| Explore Courses for JEE exam | |
Top Courses for JEE
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
