Question

Question 9 of 10Graph the solution to the following system of inequalities.x² + y² ≤9-x+y>3y

Answer 1

Given: A system of linear inequalities-

`\begin{gathered} x^2+y^2\leq9 \\ -x+y>3 \end{gathered}`

Required: To graph the solution to the system of inequalities.

Explanation: The first inequality represents the area inside a circle of radius 3 units having a center at the origin as the general equation of a circle is-

`x^2+y^2=r^2`

The second inequality represents the area above a straight line having a slope of 1 and y-intercept of 3. This can be seen by writing the equation in slope-intercept form-

`y=mx+c`

Hence, the graph of the system of inequalities is-