# How do you solve 3x+y<=6?

Jul 20, 2018

#### Explanation:

Solving linear inequalities in $2$ variables is done graphically.

Any point lying in the shaded area, will comply to the inequality.

Take, for example, the point $\left(- 5 , 2\right)$ which is in the shaded area

Then,

$3 x + y = 3 \cdot - 5 + 2 = - 13$

And this is $\le 6$

Take, for example, the point $\left(5 , 5\right)$ which is outside the shaded area

Then,

$3 x + y = 3 \cdot 5 + 5 = 25$

And

This does not comply to the conditions

$3 x + y \le 6$

graph{3x+y-6<=0 [-16.02, 16.01, -8.01, 8.01]}