Question

Examine the following system of inequalities.

{y > −x + 4 and y ≤−(1/2)^x + 6
Which graph shows the solution to the system?

Dotted linear inequality shaded below passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded above passes through (negative 1, 8) & (0, 7).

Dotted linear inequality shaded below passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).

Dotted linear inequality shaded above passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded below passes through (negative 1, 8) & (0, 7).

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).

Answer 1

A i think

Explanation:

Answer 2

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Explanation:

we have

`y > -x+4` ----> inequality A

The solution of the inequality A is the shaded area above the dotted line
`y=-x+4`

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

`y \leq -(1/2)^(x) +6` -----> inequality B

The solution of the inequality B is the shaded area above the solid line
`y=-(1/2)^(x) +6`

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)