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MODULE 4: LINEAR INEQUALITIES IN TWO

VARIABLES

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>12x+3y>1

?
2⋅1+3⋅2> 12⋅1+3⋅2> 1
?
?
2+5> 12+5> 1
?
7>17>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.

Example

Graph the inequality

y≥−x+1y≥−x+1