Question

Solve the system of two linear inequalities graphically.- 2y < - 4x – 16- 5y > 5x + 50Step 1 of 3: Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.Choose the type of boundary line:DashedO Solid (-) O3Enter two points on the boundary line:10-50.000Select the region you wish to be shaded:ОАB10

Answer 1

`\begin{cases}-2y<-4x-16 \\ -5y\ge5x+50\end{cases}`

1. Solve the inequalities for y:

First ineqaulity: divide both sides of the inequality by -2 (as you divide by a negative number the inequality sing change to the opposite):

`\begin{gathered} (-2)/(-2)y>(-4)/(-2)x-(16)/(-2) \\ \\ y>2x+8 \end{gathered}`

Second inequality: divide both sides of the inequality by -5:

`\begin{gathered} (-5)/(-5)y\le(5)/(-5)x+(50)/(-5) \\ \\ y\le-x-10 \end{gathered}`

2. Define the kind of boundary line for each inequality:

When the inequality is < or > the boundary line is a dashed line.

When the inequality is ≥ or ≤ the boundary line is a solid line.

First inequality: as the inequality sing is > the boundary line is a dashed line.

Second inequality: as the inequality sing is ≤ the boundary line is a solid line.

3. Find two points (x,y) for each boundary line:

First inequality:

Line:

`y=2x+8`

Find x when y is 0:

`\begin{gathered} 0=2x+8 \\ 0-8=2x+8-8 \\ -8=2x \\ -(8)/(2)=(2)/(2)x \\ \\ -4=x \end{gathered}`

Point (-4,0)

Find y when x is 0:

`\begin{gathered} y=2(0)+8 \\ y=0+8 \\ y=8 \end{gathered}`

Point (0,8)

______________

Second inequality:

Line:

`y=-x-10`

Find x when y is 0:

`\begin{gathered} 0=-x-10 \\ 0+10=-x-10+10 \\ 10=-x \\ (-1)\cdot10=(-1)\cdot(-x) \\ -10=x \\ \\ x=-10 \end{gathered}`

Point (-10,0)

Find y when x is 0: