Q2. - Algebra 2

Question

Solve each system of inequalities by graphing.2

$\begin{array}{c}y\ge 3x-4\\ y\le x+3\end{array}$

Step-by-Step Solution

Answer

The solution of the system of inequalities is

Step-1 –Concept of solving the linear inequalities

To solve the inequalities we convert the inequalities into linear equations and find the solutions of the equations to obtain the graph.

Step-2 –Concept of shading the region

For shading the region, we choose a point. If the point satisfies the inequalities then the shaded region is towards the point otherwise, the shaded region is away from the point.

Step-3 –Solving the inequalities

Given inequalities are$3x-4\le y\le x+3.$

Their respective linear equations are$y=3x-4$  and $y=x+3.$

The points which satisfy the equation $y=3x-4$  are$(0,-4)$  and .$(1,-1)$

The points, which satisfy the equation$y=x+3$ are$(0,3)$ and $(-3,0).$

Step-4 –Evaluating the shaded region

We choose$(0,0)$ to get the shaded region. The point  $(0,0)$ satisfies both the inequalities .$y\ge 3x-4,y\le x+3$

Step-5 –Plotting the graph

Therefore, the graph for the inequalities is

The common shaded region is $3x-4\le y\le x+3.$