Question

4x + 3y = 6 -4x + 2y = 14 Solve the system of equations. Responses A x = , y = 3x = 1 2 , y = 3 B x = 3, y = x = 3, y = 1/2 C x = 4, y = - x = 4, y = - 3/2 D x = 4, y = - x = 4, y = - 10/3 E x = - , y = 4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of elimination by multiplying one or both equations to get equal coefficients for either x or y.

Here, we can eliminate x by multiplying the first equation by 1 and the second equation by 4:

(1) 4x + 3y = 6
(2) -4x + 2y = 14

After multiplying, the equations become:

(3) 4x + 3y = 6
(4) -16x + 8y = 56

Now, we can add equation (3) and equation (4):

(3) 4x + 3y = 6
(4) -16x + 8y = 56
-----------------------
11y = 62

If we divide both sides of equation (5) by 11:

11y/11 = 62/11
y = 62/11
y = 6

Now we substitute the value of y back into any of the original equations. Let's use equation (1):

4x + 3(6) = 6
4x + 18 = 6
4x = 6 - 18
4x = -12
x = -12/4
x = -3

So the solution to the system of equations is:

x = -3
y = 6

Therefore, the correct answer is:

x = -3, y = 6

Answer 2

is that correct?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in my previous response. Upon reviewing the equations, it appears I made an error. Let's solve the system correctly:

Given the system of equations:
4x + 3y = 6 ... (1)
-4x + 2y = 14 ... (2)

To eliminate x, we can add equation (1) and equation (2):

(4x + 3y) + (-4x + 2y) = 6 + 14
4x - 4x + 3y + 2y = 20
5y = 20

Dividing both sides of equation (3) by 5:
5y/5 = 20/5
y = 4

Now we substitute the value of y back into equation (1):

4x + 3(4) = 6
4x + 12 = 6
4x = 6 - 12
4x = -6
x = -6/4
x = -3/2

So, the correct solution to the system of equations is:
x = -3/2
y = 4

Therefore, the answer is:
x = -3/2, y = 4

The correct response is:
C) x = -3/2, y = 4.