Answer: All points in the shaded region after 2y<-12x+4 is the solution.
Step-by-step explanation:
Since we have given that
[tex]2y<-12x+4 \\\\and\\\\y<-6x+4[/tex]
We need to find the point of solution to the system of inequalities:
Suppose
[tex]2y=-12x+4\\and\\y=-6x+4[/tex]
We first check the consistency of the system of equation:
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\\\\\frac{2}{1}=\frac{-12}{-6}=\frac{4}{4}\\\\2=2\neq 1[/tex]
So, it is parallel system of equations, but we consider it as an inequality, so all the points in the shaded region is the solution.
Using zero test,
[tex]2y<-12x+4[/tex]
0<4 it is true so, shaded part is towards the center.
Similarly,
[tex]y<-6x+4[/tex]
0<4 again it is true it would be shaded towards the center.
So, the common part will be after 2y<-12x+4 .
Hence, all the points in the shaded region is the solution.
