Question
Mathematics
Which graph shows the solution to the system of linear inequalities? y < =2x – 5 y > –3x + 1
Solve problem with AI

The graph of system of inequality $$\left\{ \begin{gathered}y \leq2x - 5\hfill \y >-3x + 1 \hfill \\ \end{gathered} \right$$ is shown below in Figure 2.

Further Explanation:

The system of inequalities is,

\left\{\begin{aligned}y\leq 2x-5\hfill \y >-3x + 1 \hfill \end{gathered} \right

The graph of the equations corresponding to the inequalities is shown in Figure 1.

Graph:

The given inequalities are,

$$y \leq2x - 5$$                                             …… (1)

$$y >-3x + 1$$                                                   …… (2)

Use test points to satisfy the inequality (1).

Consider the test points $$\left( {0,0}\right)$$ to check whether the points satisfy the inequality (1).

Substitute 0 for $$x$$ and 0 for $$y$$ in inequality (1) to check that the point $$\left( {0,0}\right)$$ satisfy the inequality (1) as,

\begin{aligned}\hfill0\mathop\leq\limits^?2\left( 0 \right)-5 \hfill 0\mathop\leq \limits^?-5{\text{}} \hfill 0\leq-5\left({{\text{False}}} \right) \\ \end{aligned}

The point $$\left( {0,0} \right)$$ is not a part of the graph and lies above the line $$y =2x-5$$.

Use test points to satisfy the inequality (2).

Consider the test points $$\left( {0,0} \right)$$ to check whether the points satisfy the inequality (2).

Substitute 0 for $$x$$ and 0 for $$y$$ in inequality (2) to check that the point $$\left({0,0}\right)$$ satisfy the inequality (2) as,

$$\begin{gathered}\hfill\left(0\right)\mathop>\limits^?-3\left(0 \right)+1{\text{}}\hfill0\mathop>\limits^?0+ 1{\text{ }}\hfill {\text{}}0 >1{\text{ }}\left( {{\text{False}}}\right){\text{}} \\ \end{gathered}$$

The point $$\left( {0,0} \right)$$ is not a part of the graph and lies below the line $$y = 2x - 5$$.

The graph of the solution set is the shaded region as shown in Figure 2.

From Figure 2, it is observed that the dark shaded region is the solution of the set of inequality $$\left\{\begin{gathered}y \leq 2x - 5 \hfill \y >-3x + 1 \hfill \\ \end{gathered}\right$$.