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<(4)/(3)x+(6)/(3) \\ y\lt(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(-7)/(7)-(4x)/(7) \\ \\ y\leqslant-(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