Question

Solve this question;

2y < 4x - 6, x < 2y + 2

And plot a graph.

Answer 1

Answer:

$y<2x-3,\:y>\dfrac{x-2}{2}\quad :\quad \begin{bmatrix}y<2x-3\\ y>\dfrac{x-2}{2}\end{bmatrix}\quad \mathrm{Unbounded}$

Step-by-step explanation:

$\begin{bmatrix}2y<4x-6\\ x<2y+2\end{bmatrix}$

$\black{\mathrm{Isolate}\:y\:\mathrm{for}\:2y<4x-6}$

$2y<4x-6$

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

$\dfrac{2y}{2}<\dfrac{4x}{2}-\dfrac{6}{2}$

$\gray{\mathrm{Simplify}}$

$y<2x-3$

$\black{\mathrm{Isolate}\:y\:\mathrm{for}\:x<2y+2}$

$x<2y+2$

$\gray{\mathrm{Switch\:sides}}$

$2y+2>x$

$\gray{\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}}$

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

$\gray{\mathrm{Simplify}}$

$2y>x-2$

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

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

$\gray{\mathrm{Simplify}}$

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

$=\begin{bmatrix}y<2x-3\\ y>\dfrac{x-2}{2}\end{bmatrix}$

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

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

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

$\gray{\mathrm{See\:graph\:below/above.}}$

$\begin{bmatrix}y<2x-3\\ y>\dfrac{x-2}{2}\end{bmatrix}\quad \mathrm{Unbounded}$