Question

How many solutions does this equation have

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

This system of equations will have infinitely many solutions. This is because when we add the two equations together, we get 16x = 96, which simplifies to x = 6. Therefore, no matter the value of x, y will always be 0.

Answer 2

[AI-generated answer — Explain Bot]

To determine how many solutions this system of equations has, we need to analyze the relationship between the two equations. Let's work through the process step by step.

First, let's simplify the equations by dividing them by 2:
Equation 1: 4x - 3y = 24
Equation 2: 4x + 3y = 24

Now, observe that the coefficients of y in both equations have opposite signs. When this occurs, we can conclude that if we were to add these two equations together, the y term would cancel out:
Equation 1 + Equation 2:
(4x - 3y) + (4x + 3y) = 24 + 24
8x = 48

We are left with a single equation: 8x = 48. This equation simplifies to x = 6.

So, the system of equations has a unique solution. The value of x is 6, and to find the corresponding value of y, we can substitute x into one of the original equations. Let's use Equation 1:
4(6) - 3y = 24
24 - 3y = 24
-3y = 0
y = 0

Therefore, the solution to the system is x = 6 and y = 0.

Answer 3

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

To determine the number of solutions of the given system of equations, we need to analyze the coefficients of the variables. In this case, the coefficients of 'x' and 'y' are the same in both equations.

Let's subtract the first equation from the second equation to eliminate 'x':

(8x+6y) - (8x-6y) = 48 - 48
8x - 8x + 6y + 6y = 0
12y = 0

Simplifying the equation, we get:
12y = 0

This equation tells us that y must equal 0.

Now, substitute the value of y = 0 into either of the original equations, for example, the first equation:

8x - 6(0) = 48
8x = 48
x = 48/8
x = 6

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

Therefore, the system has one solution.