Question

First consider the system of equations y = -1/2 x + 1 and y = x - 5. Then consider the system of inequalities y > -1/2x+1 and y < x-5. When comparing the number of solutions in each of these systems, which statement is true?
Both systems have an infinite number of solutions.
The system of equations has more solutions.
The system of inequalities has more solutions.
Both systems have only one solution.​

Answer 1

we conclude that the system of inequalities has more solutions than the system of equations.

What can we conclude about the two given systems?

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

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