Question

What is the solution in the following system? {-3×-2y=-12; 9×+6y=-9

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given system of equations is:

-3x - 2y = -12 ---(1)
9x + 6y = -9 ---(2)

To solve this system, we can use the method of substitution.

From equation (1), we can rearrange it to solve for x:
-3x = -12 + 2y
Dividing all terms by -3:
x = (2y - 12)/-3
x = (12 - 2y)/3

Now, substitute the value of x in equation (2):
9((12 - 2y)/3) + 6y = -9

Multiplying through by 3 to clear the fraction:
9(12 - 2y) + 18y = -27

Expand and simplify:
108 - 18y + 18y = -27
The y terms cancel out, and we're left with:
108 = -27

This is a contradiction, which means the system of equations has no solution.

Answer 2

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

To find the solution of the system of equations:

1. Rearrange the equations in a standard form:
-3x - 2y = -12 (Equation 1)
9x + 6y = -9 (Equation 2)

2. Multiply Equation 1 by 3 and Equation 2 by -1 to create opposite coefficients for x:
-9x - 6y = 36 (Equation 3)
-9x - 6y = 9 (Equation 4)

3. Now subtract Equation 4 from Equation 3 to eliminate x:
(-9x - 6y) - (-9x - 6y) = 36 - 9
-9x - 6y + 9x + 6y = 27y = 27
0y = 27

The equation 0y = 27 implies that there is no solution to the system of equations. It means the lines represented by these equations are parallel and do not intersect.