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Sagot :
we have a system of inequalities
Inequality A
[tex]-4x+3y<6[/tex]Isolate the variable y
[tex]\begin{gathered} 3y\lt6+4x \\ y<\frac{4}{3}x+\frac{6}{3} \\ y\lt\frac{4}{3}x+2 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the dashed line y=(4/3)x+2
Inequality B
[tex]4x+7y\leq-7[/tex]Isolate the variable y
[tex]\begin{gathered} 7y\leqslant-7-4x \\ y\leqslant\frac{-7}{7}-\frac{4x}{7} \\ \\ y\leqslant-\frac{4}{7}x-1 \end{gathered}[/tex]The solution to the second inequality is the shaded area below the solid line y=-(4/7)x-1
therefore
The solution to the system of inequalities is the shaded area below the dashed line y=(4/3)x+2 and below the solid line y=-(4/7)x-1
Using a graphing tool
see the attached figure below
Remember that
If an ordered pair is a solution to the system of inequalities
then
the ordered pair must lie in the shaded region of the solution
so
the point (-2,-2) is a solution to the system of inequalities
see the figure below
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