Iwill give ! lots of !

which system of inequalities is represented by the graph?

a) y ≤ x - 5 and y ≥ -3x + 2

b) y ≤ x - 5 and y ≥ -3x - 2

c) y ≤ -x + 5 and y ≥ 3x - 2

d) y ≤ x + 5 and y ≥ -3x - 2


Iwill give ! lots of ! which system of inequalities is represented by the graph?

Answers

Option B) y ≤ x - 5 and y ≥ -3x - 2

Step-by-step explanation:

step 1

Find the equation of the inequality with y-intercept -5

The equation of the solid line has a positive slope

Take the ordered pairs (0,-5) and (4,-1) to find the slope

m=(-1+5)/(4-0)=1

The equation of the solid line is y=x-5

The solution of the inequality is the shaded area below the solid line

therefore

The equation of the first inequality is

y\leq x-5

step 2

Find the equation of the inequality with y-intercept -2

The equation of the solid line has a negative slope

Take the ordered pairs (0,-2) and (1,-5) to find the slope

m=(-5+2)/(1-0)=-3

The equation of the solid line is y=-3x-2

The solution of the inequality is the shaded area above (to the right) the solid line

therefore

The equation of the second inequality is

y\geq -3x-2

step 3

The system of inequalities is

y\leq x-5

y\geq -3x-2

Option B is the correct one.

Step-by-step explanation:

The first graph passes through the points (0,-2).

Hence, the inequality equation maybe y ≥ - 3x - 2 or y ≥ 3x - 2.

Therefore, options B, C, D can be correct.

Again, the other graph passes through the point (0,-5).

Hence, the inequality equation that can be the solution is y ≤ x - 5.

Therefore, inequality A or B can be the answer.

Hence, combining those two conditions option B is the correct one. (Answer)



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