Q40. - Algebra 2

Question

Choose the system of inequalities whose solution is represented by the graph. 

$\begin{array}{c}A.y<-2\\ x<-3\\ B.y\le -2\\ x>-3\\ C.x\le -2\\ y>-3\\ D.x<-3\\ y<-3\end{array}$

Step-by-Step Solution

Answer

The graph represents the system of inequalities $\begin{array}{c}B.y\le -2\\ x>-3\end{array}$

Step-1 &ndash; Apply the concept of graphing the inequality

The steps to graph the inequality are provided below.

1. If the inequality contains greater than or less than sign then the boundary of the line will be dashed. If the inequality contains signs of greater than or equal to or less than or equal to then the boundary of the line will be solid. 

2. Select a point (known as test point) from the plane that does not lie on the boundary on the line and substitute it in the inequality. 

3. If the inequality is true then shade the region that contains the test point otherwise shade the other region when inequality is false.

Step-2 &ndash; Interpret the lines

The lines on Cartesian are vertical and horizontal. That is one line is parallel to x-axis and one line is parallel to y-axis.

The line that is parallel to y-axis is 3 units left of origin. Also the line is dashed

The line that is parallel to x-axis is 2 units below the origin. Also the line is solid

Therefore, equation of lines are $y=-2\text{ and }x=-3$.

Step-3 &ndash; Interpret the sign of inequalities

The ordered pairs in shaded region has their x-coordinate greater than $-3$ and y-coordinate less than or equal to $-2$.

Therefore, system of inequalities formed is provided below.

$\begin{array}{c}y\le -2\\ x>-3\end{array}$

Hence, the system of inequalities that lie in shaded region is provided below.

$\begin{array}{c}B.y\le -2\\ x>-3\end{array}$