Question

Which point is a solution to the system below 2y<-12x+4 y<-6x+4?

Answer 1

Answer: All points in the shaded region after 2y<-12x+4 is the solution.

Step-by-step explanation:

Since we have given that

$2y<-12x+4 \\\\and\\\\y<-6x+4$

We need to find the point of solution to the system of inequalities:

Suppose

$2y=-12x+4\\and\\y=-6x+4$

We first check the consistency of the system of equation:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\\\\\frac{2}{1}=\frac{-12}{-6}=\frac{4}{4}\\\\2=2\neq 1$

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,

$2y<-12x+4$

0<4 it is true so, shaded part is towards the center.

Similarly,

$y<-6x+4$

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.