Question

How many solutions does the system of equations have?%0D%0A8x−6y=48%0D%0A8x+6y=48(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The system of equations can be represented as:

8x - 6y = 48
8x + 6y = 48

By adding the two equations together, the 8x terms will cancel out:

(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 6

Substituting the value of x back into one of the equations, we can solve for y:

8(6) + 6y = 48
48 + 6y = 48
6y = 0
y = 0

Therefore, there is only one solution to the system of equations, which is x = 6 and y = 0.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the number of solutions for the given system of equations, we need to determine if the equations are consistent or inconsistent.

Let's write down the system of equations:

1) 8x - 6y = 48
2) 8x + 6y = 48

We can add these two equations to eliminate the variable 'y'. Adding equations (1) and (2), we get:

(8x - 6y) + (8x + 6y) = 48 + 48

Simplifying the left side and right side of the equation:

16x = 96

Dividing both sides of the equation by 16:

x = 6

Now, substituting the value of x into either of the original equations, let's use equation (1):

8(6) - 6y = 48

Simplifying and solving for y:

48 - 6y = 48
-6y = 0
y = 0

The solution to the system of equations is x = 6 and y = 0.

Therefore, the system of equations has a unique solution, which means it is consistent and the number of solutions is 1.

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of solutions for a system of equations, we can compare the coefficients of the variables in the equations.

Let's analyze the given system of equations:

1) 8x - 6y = 48
2) 8x + 6y = 48

Notice that the coefficients of y are different in these two equations, which means they have opposite signs (one is negative and the other is positive). In this case, we can conclude that the two lines represented by these equations are parallel.

When two lines are parallel, they never intersect, so there are no common points of intersection. As a result, the system of equations has NO SOLUTIONS.

In summary, the system of equations you provided has no solutions.