Given:
The boundary line of an inequality is:
[tex]2x+3y=6[/tex]
The solution set contains (0,0).
To find:
The inequality.
Solution:
The boundary line of an inequality is
[tex]2x+3y=6[/tex]
Since (0,0) is in the solution set, therefore (0,0) satisfies the required inequality.
Taking LHS, we get
[tex]LHS=2x+3y[/tex]
Substitute x=0 and y=0.
[tex]LHS=2(0)+3(0)[/tex]
[tex]LHS=0+0[/tex]
[tex]LHS=0[/tex]
The right hand side of the given equation is 6.
[tex]RHS=6[/tex]
We know that,
[tex]0<6[/tex]
[tex]LHS<RHS[/tex]
[tex]2x+3y<6[/tex]
The boundary line is not a dotted line, it means the points on the boundary line are also included in the solution set. So, the inequality sign must be [tex]\leq [/tex].
[tex]2x+3y\leq 6[/tex]
Therefore, the required inequality is [tex]2x+3y\leq 6[/tex].
