Choose the ordered pair(s) that are solutions to the syste (There may be one or many correct options). $\newline$ $\left\{\begin{array}{l} -4 x+3 y \leq 0 \\ 8 x+2 y \leq-2 \end{array}\right.$ $\newline$ Show your work here

Full solution

Q. Choose the ordered pair(s) that are solutions to the syste (There may be one or many correct options).

\newline

\left\{\begin{array}{l} -4 x+3 y \leq 0 \\ 8 x+2 y \leq-2 \end{array}\right.

\newline

Show your work here

Simplify Inequalities: Step $1$ : Simplify the inequalities if possible. $\newline$ - First inequality: $-4x + 3y \leq 0$ $\newline$ - Second inequality: $8x + 2y \leq -2$
Solve First Inequality: Step $2$ : Solve the first inequality for $y$ . $-4x + 3y \leq 0$ $3y \geq 4x$ (by adding $4x$ to both sides) $y \geq \frac{4}{3}x$ (by dividing both sides by $3$ )
Solve Second Inequality: Step $3$ : Solve the second inequality for $y$ . $8x + 2y \leq -2$ $2y \leq -8x - 2$ (by subtracting $8x$ from both sides) $y \leq -4x - 1$ (by dividing both sides by $2$ )
Graph Inequalities: Step $4$ : Graph the inequalities to find the intersection. $\newline$ - Graph $y \geq \frac{4}{3}x$ as a shaded region above the line $y = \frac{4}{3}x$ . $\newline$ - Graph $y \leq -4x - 1$ as a shaded region below the line $y = -4x - 1$ . $\newline$ - The intersection of these regions will give the solution set.
Check Intersection: Step $5$ : Check for points of intersection or common regions. $\newline$ - The lines $y = \frac{4}{3}x$ and $y = -4x - 1$ intersect at a point. To find this point, set $\frac{4}{3}x = -4x - 1$ . $\newline$ $\frac{4}{3}x = -4x - 1$ $\newline$ $4x + 12x = -3$ (by multiplying all terms by $3$ to clear the fraction) $\newline$ $16x = -3$ $\newline$ $x = -\frac{3}{16}$ $\newline$ $y = \frac{4}{3}(-\frac{3}{16})$ $\newline$ $y = -\frac{1}{4}$