Solve the system of inequalities by graphing.
y<7/9x–3
y< –1/4x+4
Select a line to change it between solid and dotted. Select a region to shade it.
The first step is to graph the two inequalities separately. We will first graph y < 7/9x – 3:
1. Graph the line y = 7/9x – 3. This line has a y-intercept of -3 and a slope of 7/9, meaning it goes up 7 units and to the right 9 units.
2. Make the line dotted, as the inequality is just < rather than ≤.
3. Shade the region below the line, as it represents y < 7/9x – 3.
Next, we will graph y < -1/4x + 4:
1. Graph the line y = -1/4x + 4. This line has a y-intercept of 4 and a slope of -1/4, meaning it goes down 1 unit and to the right 4 units.
2. Make the line dotted, as the inequality is just < rather than ≤.
3. Shade the region below the line, as it represents y < -1/4x + 4.
The solution to the system of inequalities will be the region that is shaded on both graphs, as it satisfies both inequalities.