# Represent to solution set of each of the following in equations graphically in two dimensional plane:

**Question:**

Represent to solution set of each of the following in equations graphically in two dimensional plane:

2. *x* + 2*y* ≥ 6

**Solution:**

Converting the in equation to equation, we obtain *x* + 2*y* = 6, i.e *x* + 2*y*

Putting *y* = 0 and* x* = 0 in this equation, we obtain *x* = 6 and *y* = 3.

So, this line meets *x*-axis at (6,0) and *y*-axis at (0,3).

We plot these points and join them by a thick line. This divides the *xy* plane into two parts.

To determine the region represented by the given inequality, consider point O(0,0). Clearly,

$(0,0)$ does not satisfy inequality $x+2 y \geq 6$.

So, the region that does not contain the origin is represented by the given inequality.

Hence, the shaded region is the solution to the in equation.