Question

Which system of inequalities is shown?

a.y > x
y > 2

b. y > x
y < 2

c. y < x
y < 2

d. y < x
y > 2

Answer 1

Answer: Choice C

y < x

y < 2

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Step-by-step explanation:

The horizontal line is y = 2 since all points on this line have a y coordinate of 2. Eg: (0,2) and (5,2)

Since we shade everything below this line, we're describing the inequality y < 2. All points in the shaded region for this describe anything with a y coordinate smaller than 2. Eg: (7,1)

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At the same time, we're also shading below the line y = x to form the inequality y < x.

So that's how we end up with this system

`\begin{cases}y < x\\y < 2\\\end{cases}`

which describes the set of all points below the lines y = 2 and y = x. The dashed lines indicate that points on the boundary do not count as solution points. For example, (5,2) is not a solution because it rests on the upper horizontal boundary.