Which graph shows the solution to this system of inequalities?

4x - 2 ≥ -4
2x + y > -3

The answer is Graph Z

Step-by-step explanation:

There is a mistake in your equations. Expression 1 is not a function as is its not defined as y but looking at the graphs I can infer that is 4x-2y>=4 , but I prove it here. The graph with positive slope crosess points (-1,0) and (0,2) so the slope is

m = (2-0)/(0--1) = 2

So following the point slope form of the graph y = mx+b this graph represent y=2x+2

expressing it in the way you show it:

y=2x+2

2x - y = -2

4x-2y = -4 (multiplying by 2)

Now the solution of the problem. The solution space of a system of  inequalities is the space where the possible solutions of both equations cross. To find which graph corresponds to which equation we can express it in explicit form y = mx+b

Equation(1)

4x-2y >= -4

2y>=4x+4

y>2x+2

Equation 2

2x + y > -3

y>-2x-3

So the graph with positive slope is equation 1 and the other is equation 2.

Now, when we have a inequality that has an equal sign it means that the points of the line that defines the line are also included in the solution set. Taking this into account only Graph Y or Z are possible answers because Equation 1 has equal sign and equation 2 so in Eq 1 the line is also a set of possible solutions ( shown in the graph by the bold line without spaces between). To find the solution set, an easy way is to replace a specific point in the equations and see if the follow the equations.An easy point is (0,0)

So (0,0) in Eq 1

4x-2y>= -4

(0,0) replaced

0>= -4 . This is true so (0,0) is the solution set of Equation 1 4x-2y>= -4. So the answers are at the right of this graph.

(0,0) in Eq 2

2x + y > -3

0>-3 Is also true. So (0,0) is the solution set of Equation of 2x + y > -3. So the answers are at the right of this graph. The intersection of both areas is the one corresponding to Graph Z.

c

step-by-step explanation:

answer: a and b

step-by-step explanation: