By finding the equation of shown straight lines, we can say that
[tex]x+y\leq 5\\2x-y\leq 8\\x\geq 0\\y\geq 0[/tex]
First of all, we need to find out the equations of the pair of the straight lines shown in the figure.
What is the equation of a straight line?
[tex]y= mx+c[/tex]
Where m is the slope = [tex]= \frac{y2-y1}{x2-x1}[/tex]
And (x1,y1) and (x2,y2) are two points on the graph.
The equation of the line passing through points (5,5) is
[tex]y=\frac{5-0}{0-5} x + c\\\\y=-x+c\\\\[/tex][tex]x+y = 5[/tex]
Since it passes through the point (5,0) so this point will satisfy the equation.
Put (5,0) in the above equation.
0 = -5+ c
c= 5
Equation: [tex]x+y =5[/tex].......eq(1)
Similarly, the equation of the line passing through the points (8,8) and (0,-8) is
[tex]y= 2x-8[/tex].......eq(2)
Therefore, from the derived equations(i) and (ii), we can say that
[tex]x+y\leq 5\\2x-y\leq 8\\x\geq 0\\y\geq 0[/tex]
To get more about inequalities refer to the link,
https://brainly.com/question/11234618
