Question

How many solutions does this following system of equations have?

1: x + y = -9
2: -x - y = 9

Answer 1

The question has infinite solutions can you explain how it has infinite?

Answer 2

Solve the following system of equations by substitution: y = 5x and 8x - 3y = 35

Answer 3

The system of equations can be simplified to:

1: x + y = -9
2: x + y = -9

Since the two equations are essentially the same, they are parallel lines that never intersect. Therefore, the system of equations has no solutions.

Answer 4

I apologize for the oversight. Let's revisit the system of equations:

1: x + y = -9
2: -x - y = 9

We can solve this system of equations by adding the two equations together:

(x + y) + (-x - y) = -9 + 9
0 = 0

As you can see, the equations simplify to 0 = 0, which is a true statement. This means that the two original equations are equivalent and represent the same line. Since the lines are the same, they overlap each other and have infinite points of intersection.

Therefore, the system of equations has infinite solutions. Thank you for pointing out the error, and I hope this clarifies the situation.

Answer 5

Given the system of equations:
1: y = 5x
2: 8x - 3y = 35

We can substitute the value of y from the first equation into the second equation to solve for x:
8x - 3(5x) = 35
8x - 15x = 35
-7x = 35
x = -5

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
y = 5(-5)
y = -25

Therefore, the solution to the system of equations is x = -5 and y = -25.