Question

which of the following is a solution to system of inequalities shown below?5x+2y>19x+y>=5a. (0,0)b. (0,1)c. (5,5)d. (5,-1)

Answer 1

The solution to the system of inequalities is (5,5), option c.

Step-by-step explanation:

To find a solution to the system of inequalities, we need to check if each point satisfies both inequalities. Let's check each option:

• (0,0): Plugging this into the inequalities, we get 0 > 19 and 0 ≥ 5, which are both false. So, (0,0) is not a solution.
• (0,1): Plugging this into the inequalities, we get 2 > 19 and 1 ≥ 5, which are both false. So, (0,1) is not a solution.
• (5,5): Plugging this into the inequalities, we get 25 > 19 and 10 ≥ 5, which are both true. So, (5,5) is a solution.
• (5,-1): Plugging this into the inequalities, we get -1 > 19 and -1 ≥ 5, which are both false. So, (5,-1) is not a solution.

Therefore, the solution to the system of inequalities is (5,5), option c.

Answer 2

5x+2y>19

x+y>=5

We have to graph each inequality:

First, express them in slope-intercept form:

y=mx+b

Where:

m= slope

b= y intercept

5x+2y>19

2y>19-5x

y> (19-5x)/2

y> -5/2x +9.5

x+y ≥ 5

y≥-x+5

So, we have the equations:

y> -5/2x +9.5

y≥-x+5

Graph:

The solution to the system is the intersection of both areas (blue and red)

The only point that is inside the solution it's c. (5.5)