Question

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line g of x is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line f of x is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −2x + 3 y ≤ x + 3 y ≥ −2x + 3 y ≥ x + 3 y ≤ −3x + 2 y ≤ −x + 2 y > −2x + 3 y > x + 3

Answer 1

After solving given graph we get inequalities as,

y < -2x+6: y=x+2

So, option A is correct.

As per given information,

The coordinates of the line that passes the axis and the line equations f(x) and g(x) are shown in the graph.

Utilizing the graph and the line's formula passing two points, get the equation of the line.

y = mx + c

Equation of lines f(x) and g(x),

For f(x),

y = mx + c

y = (-)x+6

y = -2x+6

For g(x),

y = mx + c

y = (2)x+2

y=x+2

So, The inequalities are,

y < -2x+6

y=x+2

The option A is correct.

Answer 2

First option:
`\left \{ {{y\leq -2x + 3} \atop {y \leq x + 3}} \right.`

Explanation:

The missing graph is attached.

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

We can observe that:

1. Both lines have the same y-intercept:

`b=3`

2. The lines are solid, then the symbol of the inequality must be
`\leq` or
`\geq`.

3. Since both shaded regions are below the solid lines, the symbol is:

`\leq`

Based on this and looking at the options given, we can conclude that the graph represents the following system of inequalities:

`\left \{ {{y\leq -2x + 3} \atop {y \leq x + 3}} \right.`