Question

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

Answer 1

Answer: Hello mate!

we have the inequalities:

y < -2x - 1

y > - 2x + h

we want to find the value of h, according to the graph.

Let's look at the graph and see what happens to the lines when the value of x is zero.

You can see that the black part is the corresponding with the first inequality, because when x = 0 the line y = -2x - 1 passes through the point (0, - 1)

Now, when x = 0, the red line, y = -2x + h passes trough the point (0, 2), then the value of h is the y-intercept of this linear equation, and we have seen that the y-intercept is 2, then h = 2

and the inequalities are:

y < -2x - 1

y > - 2x + 2

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 $2$