Q8. - Algebra 2

Question

Solve each system of inequalities. Sketch each graph on a sheet of paper. 

8. $\begin{array}{l}\frac{1}{4}y-x\ge -2\\ \frac{1}{3}y+2x\le 4\end{array}$

Step-by-Step Solution

Answer

The shaded region is the solution of the given inequations, which is unbounded.

Step-1 –Apply the concept of linear equation to solve the linear inequation.

For, $\frac{1}{4}y-x=-2.$

If$x=2$, then$y=0$.

If$x=3$, then$y=4$.

If$x=1$, then $y=-4.$

$\therefore$The points are $\left(2,0\right),\left(3,4\right)$ and $\left(1,-4\right).$

For, $\frac{1}{3}y+2x=4.$

If$x=2$, then$y=0$.

If$x=3$, then$y=-6$.

If$x=1$, then $y=6.$

$\therefore$The points are $\left(2,0\right),\left(3,-6\right)$ and $\left(1,6\right).$

Step-2–Plot the point on the graph paper and form a region of each inequation

Step-3–Identifying the common region

Since, the solution of $\frac{1}{4}y-x=-2$is towards the origin and the solution of $\frac{1}{3}y+2x=4$is towards the origin. Therefore, the shaded region is the common region that is the solution of inequation.