Question

hello I am having difficulty on this problem please help thank you

Answer 1

we have a system of inequalities

Inequality A

$-4x+3y<6$

Isolate the variable y

$\begin{gathered} 3y\lt6+4x \\ y<\frac{4}{3}x+\frac{6}{3} \\ y\lt\frac{4}{3}x+2 \end{gathered}$

The solution to the first inequality is the shaded area below the dashed line y=(4/3)x+2

Inequality B

$4x+7y\leq-7$

Isolate the variable y

$\begin{gathered} 7y\leqslant-7-4x \\ y\leqslant\frac{-7}{7}-\frac{4x}{7} \\ \\ y\leqslant-\frac{4}{7}x-1 \end{gathered}$

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