Yeah. It
thinks it can do math, and it can mimic the style of a textbook answer, but it can't actually do the math. Here is a rather frustrating chat session I had with it:
Me: Suppose we have two unknown quantities x and y. If three time x plus two
times y is twenty, and 2 times x plus three time y is ten, what are x and y?
ChatGPT: To solve this problem, we can set up and solve a system of linear
equations. The first equation we are given is 3x + 2y = 20, and the second
equation is 2x + 3y = 10.
We can solve this system of equations using the substitution method. First, we
can solve the first equation for x in terms of y by dividing both sides of the
equation by 3 to get x = (20 - 2y) / 3. We can then substitute this expression
for x in the second equation, 2(20 - 2y) / 3 + 3y = 10, to get 40 - 4y + 3y =
10, or -y = -30. This tells us that y = 30.
We can then use this value of y to solve for x in the first equation.
Substituting y = 30 into the equation 3x + 2(30) = 20, we get 3x + 60 = 20, or
3x = -40. This tells us that x = -40 / 3 = -13.33.
Therefore, the solution to this system of equations is x = -13.33 and y = 30.
Me: Can you check your answer for me?
ChatGPT: Yes, we can check our solution by substituting the values x = -13.33
and y = 30 into the original equations to see if they are satisfied.
Substituting these values into the first equation, 3(-13.33) + 2(30) = 20, we
get -40 + 60 = 20, which is true. Substituting these values into the second
equation, 2(-13.33) + 3(30) = 10, we get -26.66 + 90 = 10, which is also true.
Therefore, our solution x = -13.33 and y = 30 satisfies both of the original
equations, and we can be confident that it is the correct solution to this
problem.
Me: Are you 100% certain that -26.66 + 90 = 10?
ChatGPT: Yes, I am confident that -26.66 + 90 = 10. This is because -26.66 is
the same as -26.66 + 0, and when we add 0 to any number, the value of the
number remains unchanged. Therefore, -26.66 + 90 is equal to -26.66 + 0 + 90,
which is equal to -26.66 + 90 = 10.
To see this more clearly, we can write out the calculation using the standard
order of operations:
-26.66 + 90 = (-26.66 + 0) + 90 = -26.66 + (0 + 90) = -26.66 + 90 = 10
We can see that at each step of the calculation, the value of the expression
remains unchanged, and we end up with the correct result of 10.
It's able to correctly set up the simultaneous set of equations, and the solution it provides even satisfies one of them. But the other is
not satisfied, and it doesn't seem to be able to notice that it's making a boneheaded arithmetic error, even when you ask it to check its work or zero in on the actual error. I wouldn't mind if it can't solve the problem, but the fact that it doubles down on trying to gaslight you into believing "-26.66 + 90 = 10" is a problem. The correct answer, by the way, is x=8, y=-2.
