What type of pair is 16x+24y=88 and 2x+3y=11?
Answer and explanation
Correct answer: Consistent and dependent
The relevant principle is that equations whose all corresponding terms have the same multiplier describe the same line. Multiply 2x+3y=11 by 8. The result is 16x+24y=88, exactly the first equation. In ratio form, 16/2=24/3=88/11=8, so the coefficients of x and y and the constants are all proportional. The two equations therefore do not impose two different conditions; they are duplicate descriptions of one line. Every point satisfying one equation satisfies the other, giving infinitely many solutions. Such a pair is called consistent and dependent, so option A is correct. It is not inconsistent, because the lines are not distinct parallel lines. It is not independent, because there is not one unique intersection point; and “unsolvable” is not appropriate when infinitely many solutions exist.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
The relevant principle is that equations whose all corresponding terms have the same multiplier describe the same line. Multiply 2x+3y=11 by 8. The result is 16x+24y=88, exactly the first equation. In ratio form, 16/2=24/3=88/11=8, so the coefficients of x and y and the constants are all proportional. The two equations therefore do not impose two different conditions; they are duplicate descriptions of one line. Every point satisfying one equation satisfies the other, giving infinitely many solutions. Such a pair is called consistent and dependent, so option A is correct. It is not inconsistent, because the lines are not distinct parallel lines. It is not independent, because there is not one unique intersection point; and “unsolvable” is not appropriate when infinitely many solutions exist.
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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