Question

Which point is a solution to the system of inequalities below?A. (1,2)B. (4,7)C. (0,3)D. (-1,1)

Answer 1

For this problem we have the following two inequalities given:

$x+2y\ge4\text{, y}-2x<0$

And we want to find the point of solution to the system of inequalities and for this case we can work with equations

$x+2y=\text{4 (1) }$$y-2x=\text{ 0 (2)}$

If we solve for x from equation (1) we got:

$x=\text{ 4}-2y\text{ (3)}$

And replacing equation (3) into equation (2) we got:

$y-2(4-2y)=\text{ 5y}-8=\text{ 0}\rightarrow y=\text{ }\frac{8}{5}=\text{ 1.6}$

And solving for x we got:

$x=\text{ 4}-(2\cdot1.6)\text{ = 0.8}$

So then the intersection point between the two lines is (0.8,1.6). If we analyze all the possible options we have this:

(1,2)