Question

How many solutions does the system have? 12x−15y=18 4x−5y=6 (1 point) Responses one solution one solution no solution no solution infinitely many solutions infinitely many solutions two solutions

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given system of equations can be solved using different methods, such as substitution, elimination, or graphing.

Let's solve the system using the method of elimination:

Multiplying the first equation by 4 and the second equation by 12, we get:
48x - 60y = 72
48x - 60y = 72

As both equations are the same, the system has infinitely many solutions.

Therefore, the correct answer is: infinitely many solutions.

Answer 2

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

To determine the number of solutions in the given system of equations, we can use the method of solving simultaneous equations.

Let's start by multiplying the second equation by 3 to cancel out the coefficients of x:

12x - 15y = 18
12x - 15y = 18

Now, subtract the second equation from the first equation:

(12x - 15y) - (12x - 15y) = 18 - 18
0 = 0

Since 0 = 0, this means that the two equations are equivalent, or they represent the same line. Therefore, the system has infinitely many solutions.

Hence, the correct answer is: "infinitely many solutions."

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of solutions of a system of linear equations, we can use the method of elimination or substitution. Let's use the method of elimination to solve this system:

Given equations:
12x - 15y = 18 --(1)
4x - 5y = 6 --(2)

We can start by multiplying equation (2) by 3 to make the coefficients of x in both equations equal:
12x - 15y = 18 --(1)
12x - 15y = 18 --(3) (3 times equation 2)

Now, we can observe that equations (1) and (3) are identical. This means that the two equations are actually representing the same line when we graph them. Since the lines coincide, there are infinitely many solutions to this system.

Therefore, the correct answer is: infinitely many solutions