# How do you solve 4x+2y<=80?

Aug 24, 2015

Solving for $x$:
$x \le 20 - \frac{y}{2}$

Solving for $y$:
$y \le 40 - 2 x$

#### Explanation:

$4 x + 2 y \le 80$

Solved for $x$.

Subtract $2 y$ from both sides.

$4 x \le 80 - 2 y$

Divide both sides by $4$.

$x \le \frac{80}{4} - \frac{2 y}{4}$

$x \le 20 - \frac{1}{2} y$$=$

$x \le 20 - \frac{y}{2}$

Solved for $y$.

Subtract $4 x$ from both sides.

$2 y \le 80 - 4 x$

Divide both sides by $2$.

$y \le \frac{80}{2} - \frac{4 x}{2}$

$y \le 40 - 2 x$

Aug 24, 2015

Solve the linear inequality in 2 variables : $4 x + 2 y \le 80$

#### Explanation:

Bring the inequality to standard form after simplification:
$2 x + y - 40 \le 0.$(1)
First, graph the line 2x + y - 40 = 0 (2) by its 2 intercepts.
Make x = 0 --> y = 40. Make y = 0 --> x = 20.
Next, solve the inequality (1) by selecting the origin O as test point. Replace x = 0 and y = 0 into inequality (1). We get -40 <= 0. It's true then the solution set area contains O. It is the area below the line (2).
Note . Because of the sign $\left(\le\right)$, the line (2) is included in the solution set.