Question

Graph the solution to the system -x+y>2 X+2y>2

Answer 1

Answer:

$\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}$

Step-by-step explanation:

Step 1: Solve the system of equations

$\begin{bmatrix}-x+y>2\\ x+2y>2\end{bmatrix}$

Isolate $y$ for $-x+y>2$

$\mathrm{Add\:}x\mathrm{\:to\:both\:sides}$

$-x+y+x>2+x$

$y>2+x$

Isolate $y$ for $x+2y>2$

$\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}$

$2y>2-x$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2y}{2}>\frac{2}{2}-\frac{x}{2}$

$y>\frac{2-x}{2}$

$\bold{=\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}}$

Step 2: Graph

Instructions for graphing:

$\mathrm{1.\:Graph\:each\:inequality\:separately.}$

$\mathrm{2.\:Choose\:a\:test\:point\:to\:determine\:which\:side\:of\:the\:line\:needs\:to\:be\:shaded.}$

$3. \mathrm{The\:solution\:to\:the\:system\:will\:be\:the\:area\:where\:the\:shadings\:}\\\mathrm{from\:each\:inequality\:overlap\:one\:another.}$

When done, it should look like this: