Which graph represents the solution to the system of inequalities?

x + y ≥ 4

2x + 3y < 12

Third graph.

Step-by-step explanation:

Given system of inequalities,

x + y ≥ 4

2x + 3y < 12

Graphing x + y ≥ 4  :

Related equation of inequality x + y ≥ 4  is x + y = 4,

Having x-intercept = (4, 0)

y-intercept = (0,4),

'≥' shows the solid line,

0 + 0 ≥ 4 ( false )

⇒ The region of inequality x + y ≥ 4 is above the line.

Graphing  2x + 3y < 12 :

Related equation of inequality 2x + 3y < 12  is 2x + 3y = 12,

Having x-intercept = (6, 0)

y-intercept = (0,4),

'<' shows the dotted line,

2(0) + 3(0) < 12 ( true )

⇒ The region of inequality 2x + 3y < 12 is below the line.

Hence, only third graph satisfies the above conditions.

Third graph is correct.

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