Question

What is the least value of x which the inequality is true? 16 is greater than or equal to -2x

Answer 1

Answer:Then the system of inequalities that represents the graph is second option:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2

Step-by-step explanation: The area shaded is below the blue line and above the red line.

1.) The blue line goes through the points:

P1=(0,3)=(x1,y1)→x1=0, y1=3

P2=(1,1)=(x2,y2)→x2=1, y2=1

Slope: m=(y2-y1)/(x2-x1)

m=(1-3)/(1-0)→m=(-2)/(1)→m=-2

Point-slope form:

y-y1=m(x-x1)

y-3=-2(x-0)→y-3=-2(x)→y-3=-2x→y-3+3=-2x+3→y=-2x+3

The area below the blue line is:

y<=-2x+3→y+2x<=-2x+3→2x+y<=3

2x +y is less than or equal to 3

2.) The red line goes through the points:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(-2,0)=(x2,y2)→x2=-2, y2=0

Slope: m=(y2-y1)/(x2-x1)

m=(0-2)/(-2-0)→m=(-2)/(-2)→m=1

Point-slope form:

y-y1=m(x-x1)

y-2=1(x-0)→y-2=1(x)→y-2=x→y-2+2=x+2→y=x+2

The area above the red line is:

y>=x+2→y-x>=x+2-x→y-x>=2

y-x is greater than or equal to 2

Then the system of inequalities that represents the graph is:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2

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