What type of pair is 12x+18y=30 and 2x+3y=5?
Answer and explanation
Correct answer: Consistent and dependent
The governing concept is the classification of a pair of linear equations by comparing the ratios of corresponding coefficients and constants. Write the equations as 12x+18y-30=0 and 2x+3y-5=0. For the first equation, each coefficient is six times the corresponding coefficient in the second: 12=6(2), 18=6(3), and 30=6(5). Thus the first equation is exactly six times the second, not a different equation. Both equations represent the same straight line, so every point on that line satisfies both equations. The pair has infinitely many solutions and is therefore consistent and dependent. Hence option A is correct. An inconsistent pair has parallel distinct lines, while an independent consistent pair has intersecting lines and exactly one solution; neither situation applies here.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
The governing concept is the classification of a pair of linear equations by comparing the ratios of corresponding coefficients and constants. Write the equations as 12x+18y-30=0 and 2x+3y-5=0. For the first equation, each coefficient is six times the corresponding coefficient in the second: 12=6(2), 18=6(3), and 30=6(5). Thus the first equation is exactly six times the second, not a different equation. Both equations represent the same straight line, so every point on that line satisfies both equations. The pair has infinitely many solutions and is therefore consistent and dependent. Hence option A is correct. An inconsistent pair has parallel distinct lines, while an independent consistent pair has intersecting lines and exactly one solution; neither situation applies here.
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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