Question

Which number completes the system of linear inequalities represented by the graph?  y < –2x – 1 and y > –2x +

Answer 1

2 is the answer because all they're asking for is b (the y-axis value) which is just where the second (red) line passes through the y-axis.

Answer 2

we have

`y\leq -2x-1` -------> inequality A

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

`y > -2x+` -------> inequality B

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

The system has no solution

we know that

The y-intercept is the value of y when the value of x is equal to zero

The y-intercept of the red line is
`2` (see the graph)

therefore

the equation of the inequality B is
`y> -2x+2`

the answer is

The number is
`2`