Question

Please help, I’m very confused

Answer 1

A) (-4, 1)

B) graph C

Explanation:

A) The point that is in the doubly-shaded area is the solution. The point at (0, 4) is on the dashed line, so is NOT a solution. See the first attachment.

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B) Look at the given inequalities. You are looking for two things:

1. which boundary line applies
2. which side of that line is shaded

Here, you can identify which line goes with which equation a couple of ways. One way is to look at the x- or y-intercept. To find the x-intercept, set y=0 and solve for x. For the first equation, that gives ...

2x ≥ -1

x ≥ -1/2

The steep line, the one that intersects the top of the graph, is the one that has an x-intercept at x = -1/2. You will also note that the solution x ≥ -1/2 means the shading is to the right of that line. (Only graphs C and D have shading to the right of that line.)

For determining which side of the line is shaded, it is useful to pick a variable term with a positive coefficient. For the second inequality, that is 2x. Considering only that term and the relationship in the inequality, we see that we have 2x ≤. This means values of x that are in the solution set are less than (or equal to) those on the boundary line. In other words, shading is to the left of the line with the shallow slope. This is true only for graphs A and C. We have already eliminated graph A, so the desired graph is C.

See the second attachment for what we're talking about here.

Answer 2

1st picture: (0,4)

The lines intersect at point (0,4).

2nd picture: Graph D

2x ≥ y - 1

2x - 5y ≤ 10

Set these inequalities up in standard form.

y ≤ 2x + 1

-5y ≤ 10 - 2x → y ≥ -2 + 2/5x → y ≥ 2/5x - 2

When you divide by a negative number, you switch the inequality sign.

Now you have:

y ≤ 2x + 1

y ≥ 2/5x - 2

Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).

In this case, it is all of them.

Next, you would look at the shaded regions.

The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.

That would mean Graph B or D.

Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.