Question

Choose the graph that represents the following system of inequalities: y ≥ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Answer 1

Answer:

Correct graph is C

Step-by-step explanation:

Given two inequalities are:

1. $y\leq -3x+1$

2. $y\leq x+3$

Step1 :  Remove the inequalities

1. $y=-3x+1$

2. $y=x+3$

Step2 :  Finding intersection points of equations

By solving linear equation

$y=-3x+1=x+3$

$-3x+x+3$

$x=-0.5$

Replacing value of x in any equations

we get,

$y=x+3$

$y=-0.5+3$

$y=2.5$

Therefore, Point of intersection is (-0.5,2.5)

Step3: Test of origin (0,0)

Here, If inequalities holds true for origin then, shades the graph towards the origin.

For equation 1.

$y\leq -3x+1$

$0\leq -3(0)+1$

$0\leq +1$

True, Shade graph towards origin.

For equation 2.

$y\leq x+3$

$0\leq 0+3$

$0\leq 3$

True, Shade graph towards origin.

Thus, Correct graph is C