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):
[tex]\begin{gathered} \frac{-2}{-2}y>\frac{-4}{-2}x-\frac{16}{-2} \\ \\ y>2x+8 \end{gathered}[/tex]Second inequality: divide both sides of the inequality by -5:
[tex]\begin{gathered} \frac{-5}{-5}y\le\frac{5}{-5}x+\frac{50}{-5} \\ \\ y\le-x-10 \end{gathered}[/tex]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:
[tex]y=2x+8[/tex]Find x when y is 0:
[tex]\begin{gathered} 0=2x+8 \\ 0-8=2x+8-8 \\ -8=2x \\ -\frac{8}{2}=\frac{2}{2}x \\ \\ -4=x \end{gathered}[/tex]Point (-4,0)
Find y when x is 0:
[tex]\begin{gathered} y=2(0)+8 \\ y=0+8 \\ y=8 \end{gathered}[/tex]Point (0,8)
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Second inequality:
Line:
[tex]y=-x-10[/tex]Find x when y is 0:
[tex]\begin{gathered} 0=-x-10 \\ 0+10=-x-10+10 \\ 10=-x \\ (-1)\cdot10=(-1)\cdot(-x) \\ -10=x \\ \\ x=-10 \end{gathered}[/tex]Point (-10,0)
Find y when x is 0:
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