Answer:
The graph in the attached figure
Step-by-step explanation:
The complete question is
Which graph best represents the solution to the following system?
5x - 2y < (less than or equal to) 10
x + y < 5
we have
[tex]5x-2y\leq 10[/tex] ----> inequality A
isolate the variable y
Adds 2y both sides
[tex]5x \leq 10+2y[/tex]
Subtract 10 both sides
[tex]5x-10 \leq 2y[/tex]
Divide by 2 both sides
[tex]2.5x-5 \leq y[/tex]
Rewrite
[tex]y \geq 2.5x-5[/tex]
The solution of the inequality A is the shaded area above the solid line
The equation of the solid line is [tex]y=2.5x-5[/tex]
The slope of the solid line is positive [tex]m=2.5[/tex]
The y-intercept of the solid line is (0,-5)
The x-intercept of the solid line is (2,0)
[tex]x+y < 5[/tex] -----> inequality B
Isolate the variable y
Subtract x both sides
[tex]y < -x+5[/tex]
The solution of the inequality B is the shaded area below the dashed line
The equation of the dashed line is [tex]y=-x+5[/tex]
The slope of the dashed line is negative [tex]m=-1[/tex]
The y-intercept of the dashed line is (0,5)
The x-intercept of the dashed line is (5,0)
using a graphing tool
The solution of the system of inequalities is the shaded area between the solid line and the dashed line
see the attached figure
