Solve the system of inequalities by graphing.
4x+3y≤21
–x+7y≤28
Select a line to change it between solid and dotted. Select a region to shade it.
The first inequality is 4x + 3y ≤ 21, so we will first graph the line 4x + 3y = 21 and shade below it.
To graph this line, we first rewrite it in slope-intercept form: y = (-4/3)x + 7. This gives us the y-intercept of 7 and the slope of -4/3.
Next, we graph the line and shade below it:
Next, we do the same for the second inequality, -x + 7y ≤ 28. We rewrite it in slope-intercept form: y = (1/7)x + 4. This gives us the y-intercept of 4 and slope of 1/7.
Next, we graph the line and shade below it:
Finally, we shade the overlapping region of the two inequalities:
The shaded region represents the solution to the system of inequalities.