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Which of the following pairs of equations represents coincident lines on a graph?निम्नलिखित में से कौन-सा समीकरण-युग्म ग्राफ पर संपाती रेखाएँ दर्शाता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2x-3y=6\); \(4x-6y=12\)\(2x-3y=6\); \(4x-6y=12\)
In option A, every term of the second equation is twice the corresponding term of the first. Thus \(a_1/a_2=b_1/b_2=c_1/c_2\), so the lines coincide and have infinitely many solutions. Exam tip: compare all three ratios.विकल्प A में दूसरे समीकरण के सभी पद पहले समीकरण के 2 गुने हैं। अतः \(a_1/a_2=b_1/b_2=c_1/c_2\), इसलिए दोनों रेखाएँ संपाती हैं और अनंत हल होते हैं। परीक्षा में तीनों अनुपात जाँचें।
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