The graph of inequality have many solution .
What is graph of inequality?
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 ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
According to the question
The system of inequalities:
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1
values to the graph of inequalities we will have to make inequalities into equal sign
y ≥ 2x – 4
y = 2x – 4
x y
0 -4
1 -2
2 0
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.
x + 2y ≤ 7
x + 2y = 7
x y
0 3.5
1 3
2 2.5
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≤ or < is used, shade below the line.
y ≥ -2
y = -2
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.
x ≤ 1
x = 1
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≤ or < is used, shade below the line.
Therefore, the darker part in graph is common part of all 4 inequalities with point (1,-2) and (1,3) .
Hence, The graph of inequality have many solution .
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