Question

Solve the system of two linear equations.

−3x−4y=−23
3x−5y=5 (1 point)
Responses

(5,−2)
left parenthesis 5 comma negative 2 right parenthesis

(−5,−2)
left parenthesis negative 5 comma negative 2 right parenthesis

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(−5, 2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is (−5, 2)

Answer 2

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

To solve the system of two linear equations −3x−4y=−23 and 3x−5y=5, we can use the method of substitution or elimination. Let's use elimination.

First, let's multiply the second equation by -1 to eliminate the variable x:

-1 * (3x - 5y) = -1 * 5
-3x + 5y = -5

Now we can add the two equations together:

-3x - 4y + (-3x + 5y) = -23 + (-5)
-6x + y = -28

Next, let's solve for y using the equation -6x + y = -28:

y = 6x - 28

Now, substitute the value of y in terms of x into one of the original equations. Let's use the first equation −3x−4y=−23:

-3x - 4(6x - 28) = -23
-3x - 24x + 112 = -23
-27x + 112 = -23
-27x = -23 - 112
-27x = -135
x = -135 / -27
x = 5

Now, substitute the value of x back into one of the equations to solve for y. Let's use the equation y = 6x - 28:

y = 6(5) - 28
y = 30 - 28
y = 2

Therefore, the solution to the system of equations is (5, 2).

The correct response is: (5, 2)

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of two linear equations, we can use the method of substitution or elimination. Let's use the elimination method to solve this system.

First, we'll eliminate the variable "x". Multiply the first equation by 3 and the second equation by -3 to make the coefficients of "x" in both equations opposite:

Equation 1: -3x - 4y = -23 (multiply through by 3)
Equation 2: 3x - 5y = 5 (multiply through by -3)

This gives us:

-9x - 12y = -69
-9x + 15y = -15

Next, subtract the two equations to eliminate the "x" variable:

(-9x - 12y) - (-9x + 15y) = -69 - (-15)
-9x - 12y + 9x - 15y = -69 + 15
-27y = -54

Now, divide both sides of the equation by -27 to solve for "y":

-27y / -27 = -54 / -27
y = 2

We have found the value of "y" to be 2. Now, substitute this value back into one of the original equations (Equation 1 or Equation 2) to solve for "x". Let's substitute it into Equation 1:

-3x - 4(2) = -23
-3x - 8 = -23
-3x = -23 + 8
-3x = -15

Divide both sides of the equation by -3 to solve for "x":

-3x / -3 = -15 / -3
x = 5

So, the solution to the system of equations is (5, 2).

Therefore, the correct response is:
(5, 2)
left parenthesis 5 comma 2 right parenthesis