Mathematics

Mathematics

Problem

Which of the following is a linear inequality in two variables? a) x2+y<9x^2 + y < 9 b) 3x+5y≥73x + 5y \ge 7 c) 4x−2≥04x - 2 \ge 0 d) xy>5xy > 5
Intuitive explanation

A linear inequality in two variables is just a linear equation (like ax+by=cax + by = c) where you replace the equals sign with an inequality symbol (<,>,≤,≥<, >, \leq, \geq). The key is checking two things: does it have exactly two variables, and are both variables to the first power only (no squares, products, or other operations)? Once you spot that pattern, you'll know you've found the right answer.

Intuitive explanation

A linear inequality in two variables is just a linear equation (like ax+by=cax + by = c) where you replace the equals sign with an inequality symbol (<,>,≤,≥<, >, \leq, \geq). The key is checking two things: does it have exactly two variables, and are both variables to the first power only (no squares, products, or other operations)? Once you spot that pattern, you'll know you've found the right answer.

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