Solve the system of inequalities by graphing.
y>6x–1
–
x+5y≤5
To graph these inequalities, we first need to rewrite them in slope-intercept form (y = mx + b).
1. y > 6x - 1:
We start by graphing the line y = 6x - 1. To do this, we plot the y-intercept at (0, -1) and use the slope of 6 to find another point (move up 6 and over 1). We then draw a dashed line to represent y > 6x - 1.
2. -x + 5y ≤ 5:
We rewrite this inequality in slope-intercept form:
5y ≤ x + 5
y ≤ (1/5)x + 1
We plot the y-intercept at (0, 1) and use the slope of 1/5 to find another point (move up 1 and over 5). We then draw a solid line to represent y ≤ (1/5)x + 1.
To determine the region of the graph that satisfies both inequalities, we shade the area below the solid line of the second inequality (since it is less than or equal to), and above the dashed line of the first inequality (since it is greater than).
The solution set is the area where the shaded regions overlap on the graph.