Question

Which graph represents the solution set of the system of inequalities?

{3y≤2x+6
2x+y>0

Answer 1

I believe the first graph represents the solution

Answer 2

First graph

Explanation:

Given equations :
`3y \leq 2x+6\,,\,2x+y > 0`

We need to find which graph represents the solution set of the given system of inequalities .

Put point (1,0) in inequation
`3y \leq 2x+6` , we get
`0\leq 8` which is true, so solution is region towards the point (1,0) i.e, region below the line 2x+6 = 3y

Put point (1,0) in inequation
`2x+y > 0`, we get
`2> 0` which is true, so solution is region towards the point (1,0) i.e, region towards the right of equation .

As we take intersecting part of both the regions , we get the shaded part as shown in the given figure .

So, answer is first graph