Question

Which region represents the solution to the given system of inequalities?

x+3y<-3
x>3

Answer 1

Answer with explanation:

The given inequalities are

  x +3 y < -3-------(1)

 x > 3--------(2)

To draw the inequality (1), we would represent the inequality in slope intercept  form and find points where it cuts the x axis and y axis.

$\frac{x}{-3}+\frac{y}{-1}=1$

It cuts the X axis at , (-3,0) and y axis at (-1,0).

Now, to determine which area need to get shaded, put, x=0 and , y=0 in inequality 1

0 +3 ×  0 < -3

0 <-3

So, for (0,0) this inequality does not hold true.

So,which shade region not including point , (0,0).

To plot inequality , 2, draw line, x=3, cutting x axis at (3,0), and shade area on right.

The Intersection of inequalities gives the required region.