What type of pair is 14x+21y=70 and 2x+3y=10?
Answer and explanation
Correct answer: Consistent and dependent
The governing idea is the ratio test for a pair of linear equations. Compare 14x+21y=70 with 2x+3y=10. Multiplying the second equation by 7 gives 7(2x+3y)=7(10), hence 14x+21y=70, which is exactly the first equation. Equivalently, the coefficient and constant ratios are 14/2=21/3=70/10=7. Since all three ratios are equal, the two equations represent coincident lines rather than two separate lines. Consequently, the system has infinitely many common solutions and is classified as consistent and dependent. Thus option A is correct. Option B would require parallel distinct lines, which would have equal coefficient ratios but an unequal constant ratio. Option C would require unequal coefficient ratios, and “unsolvable” is not the standard classification for this case.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
The governing idea is the ratio test for a pair of linear equations. Compare 14x+21y=70 with 2x+3y=10. Multiplying the second equation by 7 gives 7(2x+3y)=7(10), hence 14x+21y=70, which is exactly the first equation. Equivalently, the coefficient and constant ratios are 14/2=21/3=70/10=7. Since all three ratios are equal, the two equations represent coincident lines rather than two separate lines. Consequently, the system has infinitely many common solutions and is classified as consistent and dependent. Thus option A is correct. Option B would require parallel distinct lines, which would have equal coefficient ratios but an unequal constant ratio. Option C would require unequal coefficient ratios, and “unsolvable” is not the standard classification for this case.
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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