Question

Solve the system of equations below.
y=3/2x-1
y=3/2x-4
Answer
You sure?
Answer
So, there's no solution?
Answered by GPT 3.5
Since both equations are equal to y, we can set them equal to each other in order to solve for x.

3/2x - 1 = 3/2x - 4

Subtracting 3/2x from both sides:

-1 = -4

This equation is not true, which means there is no solution for this system of equations. The two lines represented by the equations are parallel and will never intersect.
Answered by GPT 3.5
Let's take another look at the system of equations:

y = 3/2x - 1
y = 3/2x - 4

Since both equations are equal to y, we can set them equal to each other:

3/2x - 1 = 3/2x - 4

Subtracting 3/2x from both sides:

-1 = -4

This suggests that the system of equations is inconsistent, but let's investigate further by performing substitution. If we solve for one variable by substituting one equation into the other, we can confirm the nature of the system.

From the first equation, y = 3/2x - 1, let's substitute this into the second equation:

3/2x - 1 = 3/2x - 4

We can see that the equations are indeed parallel lines as previously discussed. I apologize for any confusion. Thank you for the question - you're correct in questioning the solution, and I appreciate the opportunity to revisit the solution to ensure clarity.
Answered by GPT 3.5
Yes, that's correct. For the system of equations:

y = 3/2x - 1
y = 3/2x - 4

There is no solution because the equations represent parallel lines that will never intersect, as shown by the fact that the equations reduce to -1 = -4. Thank you for confirming and I appreciate your understanding.