Graph the given system and determine the vertices of the overlapping region.
(- 4,6), (- 3,8), (4.8,- 7.6), (8/7,-66/7)
Practice makes perfect
Let's begin by graphing each inequality. Then, we will identify the overlapping region and find the coordinates of the vertices.
Inequality I
Let's graph the first inequality. By exchanging the inequality symbol to an equals sign, we can find the boundary line. Then, we will rewrite the equation in slope-intercept form.
Inequality: 2y-x≥- 20
Boundary Line: 2y-x=- 20
Slope-Intercept Form: y=1/2x-10
The y-intercept of this boundary line is - 10 and the slope is 12. The line will be solid as the inequality is not strict. Let's test the point ( 0, 0).
Once more, the point satisfied the inequality so we will shade the region that contains the point.
Inequality III
We will follow the same process for the third inequality. The boundary line is y=- 2x+2. Next, to determine which region to shade, we will test the point ( 0, 0).
Thus, we will shade the region that includes the point.
Combining the Inequality Graphs
Let's draw the graphs of the inequalities on the same coordinate plane and highlight the vertices.
To determine the first vertex we have to find the points of intersection of the boundary lines. Let's calculate the vertex formed by y=- 3x-6 and y=2x+14. To do this, we have to solve the system of equations related to these lines.
