Question

Which system of the inequalities represents the graph?

Answer 1

Answer: D

Explanation:

That line on the right is x=2 but the shaded area is less than 2 so one part is: x≤2

which eliminates A and C

then the line on top has a y-intercept at 2 and has a slope of 1, i plug that into y=mx+b where m=1 and b=2

y=x+2 and the shaded area is under that line so y<x+2

Which would eliminate B

so D is my answer

Answer 2

Answer: The fourth / bottom answer.

Explanation:

To find the answer to this question, we will see which inequalities graphed represent the graph, as asked. We will write equations for the lines in the graph, then see which answer option lines up with the equations we find.

The vertical line can be represented by x ≤ 2

➜ The solid line tells us it will be a ≤ or ≥ symbol because it's also equal to. Since the shading is left of the line, it's less than or equal to.

➜ This rules out the first and third answer options.

Next, we will look at the two diagonal lines. These equations are written in slope-intercept form. The line graphed on top can be represented with y < x + 2

➜ The dashed line tells us it will be a < or > symbol because it's not equal to. Since the shading is below the line, it is less than or equal to.

➜ This rules out the second option.

The line graphed on top can be represented with y > -
`(1)/(4)`x - 3

➜ The dashed line tells us it will be a < or > symbol because it's not equal to. Since the shading is above the line, it is greater than or equal to.

➜ This leaves us with the fourth answer option as our answer.

The only answer option that aligns with the equations we found above is;

The fourth / bottom answer.

x ≤ 2

y < x + 2

y > -
`(1)/(4)`x - 3