Let's analyze the given system of inequalities.
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Inequality 1: y-2x≤ 4
Inequality 2: 6x-3y -12
We are asked to fill with <, ≤, >, or ≥, so that the given system has no solution. Therefore, the solutions of each inequality should be completely different. Notice that the coefficients in both inequalities are proportional. Let's multiply Inequality 1 by - 3.
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Inequality 1: y-2x≤ 4
Inequality 2: 6x-3y -12
⇓
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Inequality 1: 6x-3y≥ - 12
Inequality 2: 6x-3y -12
Notice that the both inequalities looks almost the same. Since we want the system to have no solutions, the signs should be opposite. Therefore, we should fill with <.
6x-3y < -12
