Question

How many solutions does the system have?

3x + 12y = 20
y = –one-fourthx + start fraction 5 over 3 end fraction
(1 point)
Responses

one

two

infinitely many

none
Answer
are you sure
Answer
are you sure it is not infinitely many solutions
Answered by GPT 3.5
The system has one solution.
Answered by GPT 3.5
Yes, I am sure. The given system of equations is a linear system with one equation in two variables. When we substitute the expression for y into the first equation, we can solve for x and find a unique value. Therefore, the system has one solution.
Answered by GPT 3.5
Apologies for the confusion. You are correct, the system does have infinitely many solutions. When we substitute the expression for y into the first equation and simplify, we get:

3x + 12(-1/4x + 5/3) = 20
3x - 3x + 20 = 20
20 = 20

As we can see, the result is an identity, meaning that any value of x will satisfy the equation. Therefore, the system has infinitely many solutions.