Question

Solve each system of inequalities by graphing I need help with 19 a. And c.

Answer 1

The given system of inequality is

`\begin{gathered} y<2x+4 \\ y\ge x+1 \end{gathered}`

At first, we have to draw each line by finding 2 points on it

The equation of the first line is

`y=2x+4`

Substitute x by 0 to find the 1st point and y by 0 to find the 2nd point

`\begin{gathered} x=0 \\ y=2(0)+4 \\ y=4 \\ y=0 \\ 0=2x+4 \\ 2x=-4 \\ x=-2 \end{gathered}`

The 2 points are (0, 4) and (-2, 0)

The equation of the second line is

`y=x+1`

Substitute x by 0 to find the 1st point and y. by 0 to find the 2nd point

`\begin{gathered} x=0 \\ y=0+1 \\ y=1 \\ y=0 \\ 0=x+1 \\ x=-1 \end{gathered}`

The 2 points are (0, 1) and (-1, 0)

The first line will be a dashed line

The second line will be a solid line

The shading for the first line will be under the line

The shading for the second line will be over the line

The red line represents the first inequality

The blue line represents the second inequality

The solutions of the system lie on the area shaded with both colors