Question

The solutions of the set of inequations 2x+y > 12, 5x + 8y > 74, x + 6y > 24, x > 0, y > 0 are​

Answer 1

The solutions are y > -2x + 12,  y > -0.625x + 9.25, x > 0, y > 0.

• An inequation is a claim that one quantity or algebraic expression has a value that is not equal to another. A linear inequation in that variable is an equation with just one variable and a single highest power.
• The inequality sign in a linear inequation replaces the equality sign in a linear equation exactly.
• The graphic representation of an equation's solution set is a number line. First, solve the linear equation. Once you've identified the solution set, mark it on the number line with a dot. If the solution set is infinite, add three more dots to denote the infinite nature of the solution set.

According to the given information, the set of inequations are,

2x+y > 12, 5x + 8y > 74, x + 6y > 24, x > 0, y > 0.

Now, 2x+y-12 > 12+(-12), 5x + 8y -74 >74-74, x+6y-24>24-24, x > 0, y > 0.

Or, 2x + y - 12 > 0, 5x + 8y - 74 > 0, x + 6y - 24 > 0, x > 0, y > 0.

Or, y > -2x + 12,  y > -0.625x + 9.25, x > 0, y > 0.

Hence, the solutions are y > -2x + 12,  y > -0.625x + 9.25, x > 0, y > 0.

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