Question

which system of linear inequalities is represented by this graphed solution?

A. y > -1/2x + 2
y ≤ 3x - 1

B. y < -1/2x + 2
y ≥ 3x - 1

C. y > -2x + 2
y ≤ 1/3x - 1

D. y ≤ -1/2x + 2
y < 3x - 1​

Answer 1

Answer:

           B.    y < -1/2x + 2  

                   y ≥ 3x - 1

Step-by-step explanation:

The gray shadowed area is below descending function and the line is dashed.

It means coefficient x is m<0 and the sign of inequality is y <  

So the inequality wich  fit it is  y < -1/2x + 2

The blue shadowed area is above ascending function and the line is uninterrupted.

It means coefficient x is m>0 and the sign of inequality is y ≥

So the second inequality of system (y ≥ 3x - 1)  also match.

Answer 2

The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

The standard equation of a line is expressed as y = mx + b;

• m is the slope of the line

• b is the y-intercept of the line

For the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):

m = 5+1/2-0

m= 6/2

m = 3

The equation of the line is y = 3x - 1

Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1

For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):

m = 0-2/4-0

m= -2/4

m = -1/2

The equation of the line is y = -1/2x + 2

Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2

Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

Learn more on inequality graph here: https://brainly.com/question/9774970