solve the system of two linear inequalities graphically. y<= 2x+3 y>-6x-9 find the region you wish to be shaded a, b, c or d
To solve the system of two linear inequalities graphically, we need to plot the graphs of both inequalities on the same coordinate system and identify the region shaded by both inequalities.
First, let's graph the inequality y <= 2x + 3. To do this, we can start by graphing the line y = 2x + 3, and then shading the region below the line to represent y <= 2x + 3.
The line y = 2x + 3 has a y-intercept of 3 and a slope of 2 (since the equation is in slope-intercept form y = mx + b). We can plot a few points on this line to help us draw it accurately. For example, when x = 0, y = 2(0) + 3 = 3, so one point on the line is (0, 3). When x = 1, y = 2(1) + 3 = 5, so another point is (1, 5). Once we have two points, we can draw a straight line passing through them.
Next, let's graph the inequality y > -6x - 9. To do this, we can start by graphing the line y = -6x - 9, but this time we will shade the region above the line to represent y > -6x - 9.
The line y = -6x - 9 has a y-intercept of -9 and a slope of -6. We can plot a few points on this line to help us draw it accurately. When x = 0, y = -6(0) - 9 = -9, so one point on the line is (0, -9). When x = 1, y = -6(1) - 9 = -15, so another point is (1, -15). Once we have two points, we can draw a straight line passing through them.
Now we have both lines graphed on the same coordinate system. The desired region that is shaded is where the shaded regions of both inequalities overlap. Let's label this region as "c."
In summary, the region we wish to be shaded is labeled "c."