Question

Which system of inequalities represents the graph?

Answer 1

y > x - 5

y > -5x + 6

y ≤ -0.6x + 2

Answer 2

Equation of Line in slope intercept form which cuts x axis at (a,0) and y axis at (0,b), is given by

           $\frac{x}{a}+\frac{y}{b}=1$

Equation of Line 1, which cuts  y axis at (0,2) and also passes through (5,-1) is given by

     $\frac{x}{2}+\frac{y}{3.5}=1$

Equation of Line 2, which cuts  y axis at (0,-5) and x axis at (5,0) is given by

    $\frac{x}{5}+\frac{y}{-5}=1$

Equation of Line 3, which cuts  y axis at (0,6) and x axis at (1.2,0) is given by

     $\frac{x}{1.2}+\frac{y}{5}=1$

Now we have to represent the shaded region by three lines in terms of  Inequality

To do this we will check whether Origin (0,0) ,is contained in the line or not.

Origin lies inside the Shaded region of line 1.

Origin lies above on the Shaded region of line 2 .

Origin does not lie in the shaded region of Line 3.

So, the three Inequalities which represent the shaded region are

1.→3.5x+2y<7

2→ x-y<5

3→5x+1.2y-6>0