Answer with explanation:
The given inequality in two variables is
⇒ 6 x + 3 y ≤ 12
⇒3×(2 x +y)≤ 3 × 4
Cancelling,3 from, both sides of the equation
⇒ 2 x + y ≤ 4
Writing the above linear inequality in slope intercept form of line
[tex]\rightarrow\frac{2 x}{4}+\frac{ y}{4}\leq 1\\\\\rightarrow\frac{ x}{2}+\frac{ y}{4}\leq 1[/tex]
Putting, x=0, and ,y=0 in the above inequality , to check origin lies on which side of inequality
→0+0≤ 4
→0≤ 4
Solution set will include the origin and will be on the left of line and will include the line, 2 x +y≤ 4 also.
