Question

Which graph shows the solution to the system of linear inequalities? y < =2x – 5 y > –3x + 1

Answer 1

we have

$y \leq 2x-5$ ----> inequality A

$y > -3x+1$ ----> inequality B      

Using a graphing tool

The solution of the inequality A is the shaded area below the solid line

see the attached figure N $1$

The solution of the inequality B is the shaded area above the dotted line

see the attached figure N $2$

therefore

the solution of the system of linear inequalities is the shaded area indicated in the attached figure N $3$

The answer in the attached figure N $3$

Answer 2

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

Learn more:  

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}  

brainly.com/question/1632445  

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12  

brainly.com/question/1473992  

3. what are the domain and range of the function f(x) = 3x + 5?  

brainly.com/question/3412497  

Answer Details :  

Grade: Middle School.  

Subject: Mathematics.  

Chapter: linear equation.  

Keywords:  

Inequality, test point, set of inequality, y<=2x-5, y>-3x+1, Expression, linear equation, quadratic, cubic expression, linear equation, zeros, function, substitution, origin, shaded, region, solution of inequality graph.