Question

Explain how to determine whether a point is a solution to a linear inequality?

Do all linear inequalities involve shading ? Explain

Answer 1

Answer:The solution of a linear inequality in two variables like Ax + By > C is an ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality.

Example

Is (1, 2) a solution to the inequality

2x+3y>1

2⋅1+3⋅2>?1

2+5>?1

7>1

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.

Explanation: