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Graph the solution to the following system of inequalities. Choose one point in the solution of the system and prove it
mathematically.
2x - 3y<=6
y< -1/2x
Include the graph of the system of inequalities and the proof of the solution.

Sagot :

Esther

Answer:

Step-by-step explanation:

[tex]2x - 3y\leq 6[/tex] ==> [tex]y\leq \frac{2}{3}x-2[/tex]

[tex]y < -\frac{1}{2} x[/tex]

[tex]2x - 3y\leq 6[/tex]

[tex]-2x[/tex]      [tex]-2x[/tex]

[tex]-3y\leq -2x+6[/tex]

[tex]\frac{-3y}{-3} \leq \frac{-2x+6}{-3}[/tex]

[tex]y\geq \frac{2}{3}x-2[/tex]

[tex]y\geq \frac{2}{3}x-2[/tex]  

[tex]y < -\frac{1}{2} x[/tex]

Check you answer using (-1,-1)

[tex]y\geq \frac{2}{3}x-2[/tex]

[tex]-1\geq \frac{2}{3}(-1)-2[/tex]

[tex]-1\geq -\frac{2}{3}-2[/tex]

[tex]-1\geq -\frac{2}{3}-\frac{6}{3}[/tex]

[tex]-1\geq -\frac{8}{3}[/tex]

[tex]-3(-1\geq -\frac{8}{3})[/tex]

[tex]3\geq 8[/tex]

True statement

Hope this helps!

View image Esther
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