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
----> inequality A
isolate the variable y
Adds 2y both sides
![5x \leq 10+2y](https://tex.z-dn.net/?f=5x%20%5Cleq%2010%2B2y)
Subtract 10 both sides
![5x-10 \leq 2y](https://tex.z-dn.net/?f=5x-10%20%5Cleq%202y)
Divide by 2 both sides
![2.5x-5 \leq y](https://tex.z-dn.net/?f=2.5x-5%20%5Cleq%20y)
Rewrite
![y \geq 2.5x-5](https://tex.z-dn.net/?f=y%20%5Cgeq%202.5x-5)
The solution of the inequality A is the shaded area above the solid line
The equation of the solid line is ![y=2.5x-5](https://tex.z-dn.net/?f=y%3D2.5x-5)
The slope of the solid line is positive ![m=2.5](https://tex.z-dn.net/?f=m%3D2.5)
The y-intercept of the solid line is (0,-5)
The x-intercept of the solid line is (2,0)
-----> inequality B
Isolate the variable y
Subtract x both sides
![y < -x+5](https://tex.z-dn.net/?f=y%20%3C%20-x%2B5)
The solution of the inequality B is the shaded area below the dashed line
The equation of the dashed line is ![y=-x+5](https://tex.z-dn.net/?f=y%3D-x%2B5)
The slope of the dashed line is negative ![m=-1](https://tex.z-dn.net/?f=m%3D-1)
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