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 $2$