Question

InequalitiesDONALD VANQuestion 9 of 9, Step 2 of 321/27CorrectSolve the system of two linear inequalities graphically,s 2y < 8 - 168y 2 - 7x + 56Step 2 of 3 : Graph the solution set or the second linear inequalityAnswerKeyThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (...Enter two points on the boundary line:510Select the region you wish to be shaded:

Answer 1

EXPLANATION

Since we have the system of inequalities:

$2y<8x-16\text{ \lparen1\rparen}$$8y≥-7x+56$

Isolating y from (1):

$y<4x-8$

Simplifying:

$y<4\left(x-2\right)$

Isolating y for the second equation:

$\mathrm{Divide\:both\:sides\:by\:}8$$\frac{8y}{8}\ge \:-\frac{7x}{8}+\frac{56}{8}$

Simplifying:

$y\ge \frac{-7x+56}{8}$$=\begin{bmatrix}y<4\left(x-2\right)\\ y\ge \frac{-7x+56}{8}\end{bmatrix}$

Plotting the graph:

For the second inequality, we can set the following points:

(2,0) and (3,4)