Which option is correct for (11x+3y=17) and (22x+7y=35)?
Answer and explanation
Correct answer: One unique solution
For the two linear equations, \(\frac{a_1}{a_2}=\frac{11}{22}=\frac{1}{2}\), while \(\frac{b_1}{b_2}=\frac{3}{7}\). Since these ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Therefore, option C is correct. Exam tip: if \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), a pair of linear equations has one unique solution.
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What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the two linear equations, \(\frac{a_1}{a_2}=\frac{11}{22}=\frac{1}{2}\), while \(\frac{b_1}{b_2}=\frac{3}{7}\). Since these ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Therefore, option C is correct. Exam tip: if \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), a pair of linear equations has one unique solution.
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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