Solve the system of inequalities by graphing.
16x+4y≥6
4x-8y>8
To graph the system of inequalities, we need to first convert them to slope-intercept form (y = mx + b).
For the first inequality, let's solve for y:
16x + 4y ≥ 6
4y ≥ -16x + 6
y ≥ -4x + 6/4
y ≥ -x + 3/2
For the second inequality, let's solve for y:
4x - 8y > 8
-8y > -4x + 8
8y < 4x - 8
y < 1/2x - 1
Now let's graph these inequalities on a coordinate plane:
First, graph the line y = -x + 3/2 (slope is -1 and y-intercept is 3/2), but we will graph the line as a solid line since the inequality is "greater than or equal to."
Second, graph the line y = 1/2x - 1 (slope is 1/2 and y-intercept is -1), but we will graph the line as a dotted line since the inequality is "less than."
The graph should look like this:
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The shaded region is the solution to the system of inequalities.
To determine if a point is within the shaded region, you can substitute the coordinates of the point into each inequality and check if they hold true.