Question

This graph shows the solutions to the inequalities y> 3x-2 and y<?x-10Does the system of inequalities have solutions? If so, which region containsthe solutions?108A84210-88441022 488BPopс-10A. There is a solution, and it is shown by region A.B. There is a solution, and it is shown by region C.C. There is no solution.D. There is a solution, and it is shown by region B.

Answer 1

Answer:

there is no solution (option C)

Step-by-step explanation:

Given:

y > 3/2x - 2

y < 3/2x - 10

To find:

The solution to both graphs

To determine the solution of the graphs, we will consider their slopes

`\begin{gathered} y\text{ > }(3)/(2)x\text{ - 2} \\ comparing\text{ with y = mx + b} \\ m\text{ = slope, b = y-intercept} \\ from\text{ the above, the slope = 3/2} \end{gathered}`
`\begin{gathered} y\text{ < }(3)/(2)x\text{ - 10} \\ the\text{ slope = 3/2} \end{gathered}`

The slope of both inequalities is 3/2. If the slopes of two lines are the same, the lines are said to be parallel. This means both inequalities are parallel lines

For parallel lines, there is no solution because the lines do not intersect (meet).

Since both inequalities give parallel lines, there will be no solution (option C)