The shaded region in the graph represents the solutions of this system of linear inequalities:

y 4x +

y ≤ x +

Step-by-step explanation:

step 1

Find the equation of the solid line

From the graph take the points (0,3) and (4,11)

Find the slope

The equation of the solid line in slope intercept form is equal to

we have

----> the y-intercept is the point (0,3)

substitute

therefore

The inequality is

step 2

Find the equation of the dashed line

The slope is given

From the graph take the y-intercept (0,-5)

The equation of the solid line in slope intercept form is equal to

we have

substitute

therefore

The inequality is

because the shaded region is below the dashed line

therefore

The system of inequalities is

step-by-step explanation: