What is the solution status of 4x-7y=5 and 12x-21y=17?
Answer and explanation
Correct answer: No solution
The governing concept is the consistency condition for a pair of linear equations in two variables. Write the equations in the form a₁x+b₁y+c₁=0 or compare the corresponding coefficients directly. For the x-coefficients, 4/12=1/3, and for the y-coefficients, (-7)/(-21)=1/3. Thus the two left-hand sides are proportional. However, the constants have ratio 5/17, which is not equal to 1/3. Therefore the two equations represent distinct parallel lines, so they do not intersect and have no common solution. Hence option C is correct. Infinitely many solutions would require the constant ratio to match as well; a unique solution would require unequal coefficient ratios.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
The governing concept is the consistency condition for a pair of linear equations in two variables. Write the equations in the form a₁x+b₁y+c₁=0 or compare the corresponding coefficients directly. For the x-coefficients, 4/12=1/3, and for the y-coefficients, (-7)/(-21)=1/3. Thus the two left-hand sides are proportional. However, the constants have ratio 5/17, which is not equal to 1/3. Therefore the two equations represent distinct parallel lines, so they do not intersect and have no common solution. Hence option C is correct. Infinitely many solutions would require the constant ratio to match as well; a unique solution would require unequal coefficient ratios.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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