Question

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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

Answer 1

Answer:

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

$y\leq x-5$

$y\geq -3x-2$