Question

Which graph represents the solution to the system of inequalities?

x + y ≥ 4


2x + 3y < 12

Answer 1

The second to last image

Explanation:

Put the lines in slope-intercept form and then plug in the point 0,0 to find out which side to shade. Also, the blue line must so solid because it's equation has a greater than or equal to sign instead of a regular greater than sign.

Answer 2

Third graph.

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.