System of inequalities
We want to find both inequations graph
First step
We find their limit line just by replacing ≤ or ≥ signs by "=":
1). -2x + 4y ≥ 8 → -2x + 4y = 8
2). 5x + 3y ≤ 9 → 5x + 3y = 9
We graph both lines:
For the first line [red line]
when x = 0 → -2(0) + 4y = 8 → y = 8/4 → y = 2
when y = 0 → -2x + 4(0) = 8 → -2x = 8 → x = -4
For the second line [blue line]
when x = 0 → 5(0) + 3y = 9 → 3y = 9 → y = 3
when y = 0 → 5x + 3(0) = 9 → 5x = 9 → x = 9/5
We locate both points for both lines and then we join them:
Second step
We know that when we use > and < signs, lines are broken
when we use ≤ or ≥ signs, lines are solid.
In this case we have that both lines are solid.
We know that both lines shows two possible shaded regions. We are going to check if the point (0, 0) is on their set of solutions. We replace x = 0 and y = 0, in order to find this out:
1). -2x + 4y ≥ 8 → -2(0) + 4(0) ≥ 8 → 0 + 0 ≥ 8 →0 ≥ 8
Since this is not true, the red shaded region should not pass across (0, 0):
2). 5x + 3y ≤ 9 → 5(0) + 3(0) ≤ 9 → 0 + 0 ≤ 9 → 0 ≤ 9
Since this IS true, the blue shaded region should pass across (0, 0):
Answer: the system of inequalities' answer is the purple combined region, and both lines are solid
