Which number completes the system of linear inequalities represented by the graph? y > 2x – 2 and x + 4y >

we have y≥2x-2 ------> inequality A

The inequality A is the solid red line in the graph the solution of the inequality A is the shaded area above the solid red line x+4y≥?------> inequality B The inequality B is the solid blue line in the graph the solution of the inequality B is the shaded area above the solid blue line we know that the point (0,-3) lie on the line of the inequality B. substitute the values of x and y in the equation of the line

x+4y=c

0+4*(-3)=c

c=-12

so the answer is -12

The system of linear inequalities is:

y > 2x – 2 and x + 4y > -12.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥  

We have,

When x = 0, y = 2(0) – 2 = -2.

So the point (0, -2) is on the line.

When x = 2, y = 2(2) – 2 = 2.

So point (2, 2) is on the line.

Plotting these two points and drawing a line through them gives us the graph of y = 2x – 2.

Next, let's graph x + 4y = -12 by solving for y:

x + 4y = -12

4y = -x - 12

y = (-1/4)x - 3

Again, we can plot two points on the line.

When x = 0, y = -3, giving us the point (0, -3).

When x = -4, y = -2, giving us the point (-4, -2).

Plotting these points and drawing a line through them gives us the graph of x + 4y = -12.

Thus,

The solution to the system of inequalities is the shaded region where the two graphs intersect and y > 2x – 2.

This region is shown in the attached image.

Learn more about inequalities here:

https://brainly.com/question/20383699

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