The system of inequalities is:
-x + 2y - 4 < 0
3x + 4y <= -420
The second inequality seems to be incomplete. I'll assume it should be an inequality sign (either "<", "<=", ">", or ">="). Assuming it's <=, let's graph the system of inequalities:
The system of inequalities is:
-x + 2y - 4 < 0
3x + 4y <= -420
To graph these inequalities, we'll start by graphing the boundary lines for each inequality.
For the first inequality (-x + 2y - 4 < 0), let's find its boundary line:
-x + 2y - 4 = 0
2y = x + 4
y = (1/2)x + 2
Now, for the second inequality (3x + 4y <= -420), let's find its boundary line:
3x + 4y = -420
4y = -3x - 420
y = (-3/4)x - 105
Now, let's plot these lines on the graph:
The line for -x + 2y - 4 = 0 (or y = (1/2)x + 2):
Choose two x-values and find the corresponding y-values.
Plot the points and draw the line.
The line for 3x + 4y = -420 (or y = (-3/4)x - 105):
Choose two x-values and find the corresponding y-values.
Plot the points and draw the line.