Question

Need help here plss

Answer 1

Answer:

Solutions: b, c, d, e

Not Solutions: a

Step-by-step explanation:

There are two ways to solve this problem: you could graph the system and check which points fall in the solution set or you could substitute the $x$  and $y$ values of each point into the inequalities that make up the system. I'm going to use the former because it's quicker, in my opinion.  

Step 1: Graph

Rewriting the first inequality gives us:

$2x+5y$

$5y$

$y$

To graph this, draw the line  $y=-\frac{2}{5}x +2$ and then, because the sign is " ", shade below the line and make it a dashed line. This is the red inequality on the graph.

Rewriting the second inequality gives us:

$3x-4y\geq -8$

$-4y\geq -3x-8$

$y\leq \frac{3}{4}x+2$

To graph this, draw the line  $y\leq \frac{3}{4}x+2$ and then, because the sign is " $\leq$", shade below the line and keep it a solid line. This is the blue inequality on the graph.

The solution set of the system will be the region where the two shaded areas overlap, which is the purple area.

Step 2: Check Points

Now, all we need to do is check whether each point lies in the purple region on the graph.

$(3,5)$ lies above the purple region, but it isn't in the region, so it is not a solution to the system.

$(-2,10)$ does lie in the purple region, so it is a solution to the system.

$(5,-12)$ does lie in the purple region, so it is a solution to the system.

$(-6,-8)$ does lie in the purple region, so it is a solution to the system.

Finally, $(0,0)$ lies in the purple region, so it is a solution to the system.

Hope this helps!