Question

HELP

On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.

y < 1/4 x + 3
y > -x +5

Answer 1

y =< 1/4 x + 3

Solutions are regions D and C

y >= -x +5

Solutions are B and C

So solution of the system of inequalities is region C.

Answer D. Region C

Answer 2

Region C

Explanation:

y ≤ 1/4 x + 3

y ≥ -x +5

The graph of both equations is already given .

LEts do the shading for each inequality

For shading we use test point (0,0)

`y\leq(1)/(4) x+3`

plug in 0 for x and 0 for y

`0\leq(1)/(4) (0)+3`

`0\leq+3` True

We shade the part that contains (0,0)

`y \geq -x +5`

For shading we use test point (0,0)

`0\geq -(0) +5`

`0\geq5` False

We shade the part that does not contains (0,0)

Solution to the inequality is Region C