solve the system of two linear inequalities graphically. 6x+6y<54 x>=6 find the region with points that satisfy both inequalities. select the region you wish to be shaded A, B, C or d
To graphically solve the system of two linear inequalities, let's start by graphing each inequality individually.
1) 6x + 6y < 54
First, rewrite the inequality in slope-intercept form:
6y < -6x + 54
y < -x + 9
Graphing the line y = -x + 9:
- Plot the y-intercept, which is (0, 9).
- Use the slope of -1 (coefficient of x) to find additional points. For example, if x = 1, then y = 8; if x = 2, then y = 7, etc. Connect these points to create a dashed line.
2) x ≥ 6
Since this is a "greater than or equal to" inequality, the line will be solid.
Graphing the line x = 6:
- Plot the point (6, 0) since x = 6. Draw a solid vertical line passing through this point.
Now, let's determine the region that satisfies both inequalities by shading.
Since the shaded region needs to satisfy both conditions, it should be the region to the right of the vertical line x = 6 and below the dashed line y < -x + 9.
Labeling the regions, we can see that the shaded region is Region B.
Therefore, the answer is B.