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Maximal number of solutions

Source: Saint Petersburg MO 2020 Grade 9 Problem 1

May 7, 2020
algebra

Problem Statement

What is the maximal number of solutions can the equation have max⁡{a1x+b1,a2x+b2,…,a10x+b10}=0\max \{a_1x+b_1, a_2x+b_2, \ldots, a_{10}x+b_{10}\}=0 where a1,b1,a2,b2,…,a10,b10a_1,b_1, a_2, b_2, \ldots , a_{10},b_{10} are real numbers, all aia_i not equal to 00.
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