Q6. - Algebra 2

Question

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

2. $\begin{array}{l}y+3x\ge 6\\ y-2x\le 9\end{array}$

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, $y+3x=6$

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

If$x=0$, then$y=6$.

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

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

For, $y-2x=9$

For, $x=-2$

If$x=-2$, then$y=5$.

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

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

$\therefore$The points are $\left(-2,5\right),\left(-3,3\right)$ and $\left(-4,1\right).$

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 $y+3x\ge 6$is away from the origin and the solution of $y-2x\le 9$is towards the normal. Therefore, the shaded region is the common region that is the solution of inequation.