Graph the system of linear inequalities below. $$\left\{ \begin{array} { l } x + y 4 \end{array} \right.$$

Question

Graph the system of linear inequalities below. $$\left\{ \begin{array} { l } 
x + y < 2 \
6 x + 2 y > 4
\end{array} \right.$$

Quizplus · Accepted Answer

To graph a linear inequality in two variables, we need to first graph the corresponding linear equation. The graph of $x+y=2$ is a line with slope $-1$ and $y$-intercept $2$: [asy] void axes(real x0, real x1, real y0, real y1) { draw((x0,0)--(x1,0),EndArrow); draw((0,y0)--(0,y1),EndArrow); label("$x$",(x1,0),E); label("$y$",(0,y1),N); for (int i=floor(x0)+1; i4$, we first graph the line $6x+2y=4$. This line has slope $-3$ and $y$-intercept $2$ (dividing both sides by $2$ gives $3x+y=2$): [asy] void axes(real x0, real x1, real y0, real y1) { draw((x0,0)--(x1,0),EndArrow); draw((0,y0)--(0,y1),EndArrow); label("$x$",(x1,0),E); label("$y$",(0,y1),N); for (int i=floor(x0)+1; i4$, we test the origin: $6(0)+2(0)=0<4$, so we shade the region above the line. [asy] void axes(real x0, real x1, real y0, real y1) { draw((x0,0)--(x1,0),EndArrow); draw((0,y0)--(0,y1),EndArrow); label("$x$",(x1,0),E); label("$y$",(0,y1),N); for (int i=floor(x0)+1; i

Graph the System of Linear Inequalities Below {x+y<26x+2y>4\left\{ \begin{array} { l } x + y < 2 \\6 x + 2 y > 4\end{array} \right.{x+y<26x+2y>4​

Graph the System of Linear Inequalities Below $\left\{ \begin{array} { l } x + y < 2 \\6 x + 2 y > 4\end{array} \right.$