How many solutions does the system of equations have? y=−2x+12 4y+x−20=0 (1 point) Responses No solution No solution Infinitely many solutions Infinitely many solutions One solution One solution Two solutions

Answer 1

To find the number of solutions, we can solve the system of equations.

By substitution, we have:

-y = 2x - 12 (from the first equation)

x = 4y - 20 (from the second equation)

Substituting the value of x from the second equation into the first equation, we get:

-(4y - 20) = 2x - 12

-4y + 20 = 2x - 12

-4y = 2x - 32

Dividing the equation by 2:

-2y = x - 16

Now we have two equations:

-y = 2x - 12

-2y = x - 16

Rearranging the second equation:

x - 2y = 16

We can now see that the two equations are equivalent; they represent the same line. Therefore, the system of equations has infinitely many solutions.

So, the answer is:

Infinitely many solutions

Answer 2

are you sure

Answer 3

Apologies for the confusion in my previous responses. Let's re-evaluate the system of equations to determine the number of solutions.

The system of equations is:

1) y = -2x + 12
2) 4y + x - 20 = 0

To solve this system, we can substitute the value of y from equation 1 into equation 2:

4(-2x + 12) + x - 20 = 0

Simplify the equation:

-8x + 48 + x - 20 = 0

Combine like terms:

-7x + 28 = 0

Subtract 28 from both sides:

-7x = -28

Divide both sides by -7:

x = 4

Now, substitute this value of x back into equation 1 to solve for y:

y = -2(4) + 12
y = -8 + 12
y = 4

Thus, we have found that the values of x = 4 and y = 4 satisfy both equations in the system.

Therefore, the system of equations has one solution.

Answer 4

correct

Answer 5

Great! I apologize for the confusion earlier. The correct answer is that the system of equations has one solution. Thank you for pointing that out. If you have any more questions, feel free to ask.