Question

The graph below represents which system of inequalities?

graph of two infinite lines that intersect at a point. One line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.

Your answer:

y ≤ −2x + 3
y ≤ x + 3


y ≥ −2x + 3
y ≥ x + 3


y ≤ −3x + 2
y ≤ −x + 2


y > −2x + 3
y > x + 3

Answer 1

Something that can help you figure out which system of inequalities fits the diagram is to look at the y-intercept

Equations of lines can be written as \(y=mx+b\) where b is the y intercept. If they both intersect at y=3 then you should expect both inequalities to also have 3 as their y value

\(y\le mx+3\) and/or \(y\ge mx+3\)


Something else you should note is that the question tells you both lines are solid. This only happens if the inequality includes the point

\(\ge\) and \(\le\) ---> solid line
\(>\) and \(<\) ---> dotted line

Answer 2

Once you figure out the equation of each line, you can check whether its greater or lower by looking at the side it is shaded

If its shaded to the below (the line), then its less than
If its shaded to the above (the line), then its greater

Answer 3

alright, i understand thank you .