Solve the System of @WORD x+2y<=2x+y>=0

$x + 2 y \leq 2 x + y \geq 0$

Step 1

Solve $x + 2 y \leq 2 x + y$ for $y$ .

Move all terms containing $y$ to the left side of the inequality.

Subtract $y$ from both sides of the inequality.

$x + 2 y - y \leq 2 x$

Subtract $y$ from $2 y$ .

$x + y \leq 2 x$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $x$ from both sides of the inequality.

$y \leq 2 x - x$

Subtract $x$ from $2 x$ .

$y \leq x$

Step 2

Subtract $2 x$ from both sides of the inequality.

$y \geq - 2 x$

Step 3

Find the intersection of $y \leq x$ and $y \geq - 2 x$ .

$- 2 x \leq y \leq x$

Step 4