Answer:
The common shaded region in the graph, represents the solution to the system of inequalities.
Step-by-step explanation:
The given inequalities are
[tex]x+y<3[/tex] .... (1)
[tex]-5x+2y<10[/tex] ..... (2)
The related lines of given inequalities are dotted lines, because the sing of inequalities are <.
The related equations of given inequalities are
[tex]x+y=3[/tex] .... (3)
[tex]-5x+2y=10[/tex] .... (4)
Find x-intercepts and y-intercepts of related equations.
Put x=0 in equations (3).
[tex]0+y=3[/tex]
Put y=0 in equations (3).
[tex]x+0=3[/tex]
Therefore the intercepts of equation (3) are (0,3) and (3,0).
Put x=0 in equations (4).
[tex]-5(0)+2y=10[/tex]
[tex]y=5[/tex]
Put y=0 in equations (4).
[tex]-5x+2(0)=10[/tex]
[tex]x=-2[/tex]
Therefore the intercepts of equation (3) are (0,5) and (-2,0).
Check the given inequalities by origin.
Put (0,0) in inequality (1),
[tex]0+0<3[/tex]
[tex]0<3[/tex]
Therefore, (0,0) lies in the shaded region of inequality (1).
Put (0,0) in inequality (2),
[tex]-5(0)+2(0)<10[/tex]
[tex]0<10[/tex]
Therefore, (0,0) lies in the shaded region of inequality (2).
The common shaded region in the graph, represents the solution to the system of inequalities.
The graph of the inequality illustrates the intercept and the solution to the system of inequalities.
The following can be depicted from the information:
x+y<3 ...... i
-5x+2y<10 ....... ii
It's important to know the x and y intercepts. Therefore,
x + y = 3
-5x + 2y = 10
0 + y = 3
x + 0 = 3
The intercept will be (0,3) and (3,0). Also, when y = 5, the intercept will be (0,5) and (2,0).
The graph is also attached.
Learn more about inequalities on:
https://brainly.com/question/24372553
