Q5. - Algebra 2

Question

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

$\begin{array}{l}3y\ge 6x-15\\ 2y\le -x+3\end{array}$

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.

We have,

$3y=6x-15.$

If  $x=0$, then $y=-5$.

If $x=1$, then $y=-3$.

If $x=2$, then  $y=-1.$

$\therefore$The points are $\left(0,-5\right),\left(1,-3\right)$ and $\left(2,-1\right).$

For, $2y=-x+3.$

If $x=1$, then$y=1$.

If $x=-1$, then$y=2$.

If $x=3$, then $y=0.$

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

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 $3y\ge 6x-15$ is away from the origin and the solution of$2y\le -x+3$ is also towards from the origin. Therefore, the shaded region is the common region that is the solution of inequation.