Question

Which system of inequalities is represented by the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

Answer 1

The first 2
Y=<3x
Y>-2x-1

Answer 2

Step 1

Find the equation of the inequality A (red line)

The equation of the red line is

`y=-2x-1` ------> see the x-intercept of the graph
`(-0.5,0)`

The solution of the inequality A is the shaded area above the red dotted line

so

the equation of the inequality A is

`y>-2x-1`

Step 2

Find the equation of the inequality B (blue line)

The equation of the blue line is

`y=3x` ------> see the graph, the slope is positive

The solution of the inequality B is the shaded area below the blue solid line

so

the equation of the inequality B is

`y \leq 3x`

therefore

the answer is

The system of inequalities is equal to

`y>-2x-1`

`y \leq 3x`