Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2

The lines of the inequalities are parallel, and the system of inequalities do not have any solution.

The system of inequalities are  given as:

The inequality y ≥ 2x + 1 has the following characteristics:

The inequality y ≤ 2x – 2 has the following characteristics:

See attachment for the graphs of the system of inequalities

Read more about system of inequalities at:

link

Step-by-step explanation:

Given the two inequalities:

To graph them, first of all, let us write their corresponding equations:

We now find at least 2 points each which satisfy the equations to plot the graph.

Equation :

Putting x = 0, y = 1

Putting y = 0, x = .

Two points are (0, 1) and (, 0).

Equation :

Putting x = 0, y = -2

Putting y = 0, x = 1.

Two points are (0, -2) and (1, 0).

Now, let us plot them.

Let us take a point (1, 4) and check whether it satisfies the first inequality.

Which is true.

So, The shaded region will be towards point (1,4).

Let us take a point (1, 4) and check whether it satisfies the second inequality.

So, The shaded region will be opposite to point (1,4).

Please refer to the attached graph for the answer.

No solution exists for them because there is no common shaded region.

20

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4