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The system of equations,x + y = 2 and 2x + 2y = 3 has
- a)infinitely many solutions
- b)finitely many solutions
- c)a unique solution
- d)no solution
Correct answer is 'D'. Can you explain this answer?
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Most Upvoted Answer
The system of equations,x + y = 2 and 2x + 2y = 3 hasa)infinitely many...
Explanation:
The given system of equations is:
x + y = 2 ...(1)
2x + 2y = 3 ...(2)
We can rewrite equation (2) as:
x + y = 3/2 ...(3)
No Solution:
If we compare equations (1) and (3), we see that they are inconsistent. They represent two different lines in the xy-plane that do not intersect. Hence, there is no solution to the system of equations.
Geometric Interpretation:
The system of equations can be interpreted geometrically as two lines in the xy-plane.
The first equation, x + y = 2, represents a line with slope -1 passing through the point (2, 0).
The second equation, 2x + 2y = 3, can be rewritten as x + y = 3/2, which represents a line with slope -1 passing through the point (3/2, 0).
Since these two lines are parallel, they do not intersect and there is no solution to the system of equations.
Therefore, option (D) is the correct answer.
The given system of equations is:
x + y = 2 ...(1)
2x + 2y = 3 ...(2)
We can rewrite equation (2) as:
x + y = 3/2 ...(3)
No Solution:
If we compare equations (1) and (3), we see that they are inconsistent. They represent two different lines in the xy-plane that do not intersect. Hence, there is no solution to the system of equations.
Geometric Interpretation:
The system of equations can be interpreted geometrically as two lines in the xy-plane.
The first equation, x + y = 2, represents a line with slope -1 passing through the point (2, 0).
The second equation, 2x + 2y = 3, can be rewritten as x + y = 3/2, which represents a line with slope -1 passing through the point (3/2, 0).
Since these two lines are parallel, they do not intersect and there is no solution to the system of equations.
Therefore, option (D) is the correct answer.
Community Answer
The system of equations,x + y = 2 and 2x + 2y = 3 hasa)infinitely many...
X/2x=y/2y not =2/3
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The system of equations,x + y = 2 and 2x + 2y = 3 hasa)infinitely many solutionsb)finitely many solutionsc)a unique solutiond)no solutionCorrect answer is 'D'. Can you explain this answer?
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