Answer:
See explanation
Step-by-step explanation:
1. Solve the system of two inequalities for y:
[tex]\left\{\begin{array}{l}-2x+3y>3\\ \\4x-3y<15\end{array}\right.\Rightarrow \\ \\\left\{\begin{array}{l}3y>3+2x\\ \\-3y<15-4x\end{array}\right.\Rightarrow \\ \\\left\{\begin{array}{l}y>1+\dfrac{2}{3}x\\ \\y>-5+\dfrac{4}{3}x\end{array}\right.[/tex]
2. To graph both inequalities, first draw dotted lines -2x+3y=3 and 4x-3y=15 (dotted because the signs of inequalities are both without notion "or equal to"). Then choose appropriate part, substituting the coordinates of the origin:
[tex]-2\cdot 0+3\cdot 0=0>3\ - \ \text{false}\\ \\4\cdot 0-3\cdot 0=0<15\ -\ \text{true}[/tex]
So, the origin belongs to the top part of the second inequality and to the bottom part of the first inequality. The intersection of these two regions is the solution set to the system of two inequalities (see attached diagram).
