What is the number of solutions of 12x - 7y = 5 and 18x - 11y = 8?
Answer and explanation
Correct answer: Unique solution
For equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, a unique solution exists when a1/a2 is not equal to b1/b2. In the given equations, the coefficient ratios are 12/18 = 2/3 and (-7)/(-11) = 7/11. Since 2/3 and 7/11 are unequal, the two lines have different slopes and intersect at exactly one point. Therefore, the pair has a unique solution, so option C is correct. The no-solution and infinitely-many-solution cases require parallel or coincident lines, respectively.
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What is the correct answer to this question?
Unique solution
Why is this the correct answer?
For equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, a unique solution exists when a1/a2 is not equal to b1/b2. In the given equations, the coefficient ratios are 12/18 = 2/3 and (-7)/(-11) = 7/11. Since 2/3 and 7/11 are unequal, the two lines have different slopes and intersect at exactly one point. Therefore, the pair has a unique solution, so option C is correct. The no-solution and infinitely-many-solution cases require parallel or coincident lines, respectively.
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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