104k views
4 votes
what's the answer of system of inequalities and when you connect the dots which line is broken and solid

what's the answer of system of inequalities and when you connect the dots which line-example-1
User Krischu
by
8.3k points

1 Answer

4 votes
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

what's the answer of system of inequalities and when you connect the dots which line-example-1
what's the answer of system of inequalities and when you connect the dots which line-example-2
what's the answer of system of inequalities and when you connect the dots which line-example-3
User Alex McKenzie
by
7.4k points