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The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is
- a)inconsistent
- b)consistent
- c)dependent consistent
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsis...
Solution:
We are given two linear equations as:
2x + 3y = 5 ...(i)
4x + 6y = 10 ...(ii)
We need to find whether these equations are consistent, inconsistent or dependent.
Method 1: By Graphical Method
We can plot the graph for these equations and check their intersection point.
The graph of equation (i) is a straight line passing through (0, 5/3) and (5/2, 0).
The graph of equation (ii) is a straight line passing through (0, 5/3) and (5/2, 0).
As we can see, both the lines are identical, i.e. they coincide with each other. Hence, the equations are dependent consistent.
Method 2: By Elimination Method
We can eliminate one variable from the given equations and check the value of other variable.
Multiplying equation (i) by 2, we get:
4x + 6y = 10 ...(iii)
Comparing equations (ii) and (iii), we can see that they are identical. This means that one equation is a multiple of the other equation. Hence, the equations are dependent consistent.
Therefore, the correct answer is option (C) dependent consistent.
We are given two linear equations as:
2x + 3y = 5 ...(i)
4x + 6y = 10 ...(ii)
We need to find whether these equations are consistent, inconsistent or dependent.
Method 1: By Graphical Method
We can plot the graph for these equations and check their intersection point.
The graph of equation (i) is a straight line passing through (0, 5/3) and (5/2, 0).
The graph of equation (ii) is a straight line passing through (0, 5/3) and (5/2, 0).
As we can see, both the lines are identical, i.e. they coincide with each other. Hence, the equations are dependent consistent.
Method 2: By Elimination Method
We can eliminate one variable from the given equations and check the value of other variable.
Multiplying equation (i) by 2, we get:
4x + 6y = 10 ...(iii)
Comparing equations (ii) and (iii), we can see that they are identical. This means that one equation is a multiple of the other equation. Hence, the equations are dependent consistent.
Therefore, the correct answer is option (C) dependent consistent.
Community Answer
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsis...
Important Definitions & Formulas: Pair of Linear Equations in Two Variables:
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The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsistentb)consistentc)dependent consistentd)none of theseCorrect answer is option 'C'. Can you explain this answer?
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The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsistentb)consistentc)dependent consistentd)none of theseCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsistentb)consistentc)dependent consistentd)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 isa)inconsistentb)consistentc)dependent consistentd)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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