Solve the following system of inequalities graphically: $2x + y \geq 8, x + 2y \geq 10$

(N/A) To solve the system of inequalities $2x + y \geq 8$ and $x + 2y \geq 10$ graphically,we first consider the corresponding equations:
$2x + y = 8$ ... $(1)$
$x + 2y = 10$ ... $(2)$
For equation $(1)$,if $x = 0$,$y = 8$. If $y = 0$,$x = 4$. The line passes through $(0, 8)$ and $(4, 0)$.
For equation $(2)$,if $x = 0$,$y = 5$. If $y = 0$,$x = 10$. The line passes through $(0, 5)$ and $(10, 0)$.
Since both inequalities are of the type $\geq$,the solution region for each inequality is the region on or above the respective lines.
The intersection point of the two lines is found by solving the equations:
$2(2x + y = 8) \Rightarrow 4x + 2y = 16$
Subtracting $(2)$ from this: $(4x + 2y) - (x + 2y) = 16 - 10$ $\Rightarrow 3x = 6$ $\Rightarrow x = 2$.
Substituting $x = 2$ in $(1)$: $2(2) + y = 8$ $\Rightarrow 4 + y = 8$ $\Rightarrow y = 4$.
The intersection point is $(2, 4)$.
The solution to the system is the common shaded region in the first quadrant and beyond,bounded by the lines $2x + y = 8$ and $x + 2y = 10$,including the points on the lines.