Question

How many solutions does the system of equations have?

y=−2x+12

4y+x−20=0

(1 point)
Responses

Infinitely many solutions
Infinitely many solutions

One solution
One solution

No solution
No solution

Two solutions

Answer 1

[AI-generated answer — Bot GPT 3.5]

The system of equations can be solved by substitution or elimination method.

Using the substitution method:
From the first equation, we have y = -2x + 12.
Substituting this into the second equation, we get:
4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0
-7x = -28
x = 4

Substituting the value of x into the first equation, we get:
y = -2(4) + 12
y = -8 + 12
y = 4

So, the solution to the system of equations is x = 4 and y = 4.

Therefore, the system of equations has one solution.

Answer 2

[AI-generated answer — Explain Bot]

To determine how many solutions the system of equations has, we can use various methods, such as graphing, substitution, or elimination.

Let's use substitution to solve the system of equations:

First, we'll solve the first equation for y:

y = -2x + 12

Now we substitute this expression for y in the second equation:

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

Simplifying the equation:

-8x + 48 + x - 20 = 0

-7x + 28 = 0

Next, we'll isolate the variable x:

-7x = -28

x = 4

Now substitute the value of x back into either of the original equations. Let's use the first equation:

y = -2(4) + 12

y = -8 + 12

y = 4

Therefore, the solution to the system of equations is x = 4 and y = 4.

Since we found a unique solution for both variables, the system of equations has one solution.

So, the answer is **One solution**.

Answer 3

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

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

First, let's solve the system of equations:

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

To solve the system, we can substitute equation (1) into equation (2):

4(-2x + 12) + x - 20 = 0
-8x + 48 + x - 20 = 0
-7x + 28 = 0

Next, subtract 28 from both sides:

-7x = -28

Now, divide both sides by -7:

x = 4

Substitute the value of x into equation (1):

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

Hence, the system of equations has one solution, which is x = 4 and y = 4.

Therefore, the answer is: One solution.