-2x-4y=1 12y=-6x-3

I have to find the solutions, or no solution, or infinite solutions to these two equations.

the two equations are

2x+4y = -1
6x+12y = -3

multiply the top equation by 3 to get
6x+12y = -3

They are the same equation. So, what does that mean?

-2x-4y = 1

6x + 12y = -3

I just rearranged the second equation.

Multiply the top equation by 3 and then add the two equations together.

You will get 0 = 0 which means there are an infinite number of solutions. This happens any time you get a true equation. What you will find is that any x, y values that makes the first equation true will also work in the second equation.

If you got 0 = -3 then this would be false and indicate that there are no solutions.

It’s not right ok

idk

To find the solutions, no solution, or infinite solutions to the given system of equations, you need to check if the equations are consistent, inconsistent, or dependent.

Step 1: Write the given system of equations:
Equation 1: -2x - 4y = 1
Equation 2: 12y = -6x - 3

Step 2: Rearrange Equation 2 to isolate one variable in terms of the other:
12y = -6x - 3
Divide both sides of the equation by 12:
y = (-6x - 3) / 12
Simplify:
y = -1/2x - 1/4

Step 3: Now you have two options for solving the system of equations: substitution method or elimination method. Let's use the elimination method.

Step 4: Multiply both sides of Equation 1 by 3 to make the coefficients of x terms opposite:
-2x - 4y = 1
Multiply by 3:
(-2x - 4y) * 3 = 1 * 3
-6x - 12y = 3

Step 5: Let's add both equations together:
-6x - 12y = 3 (Equation 1 multiplied by 3)
y = (-1/2)x - 1/4 (Equation 2)

Adding both equations:
-6x - 12y + y = 3 + (-1/2)x - 1/4

Step 6: Simplify the equation:
-6x - 11y = 3 - 1/2x - 1/4

Step 7: Let's rearrange the equation to solve for x:
-6x + 1/2x = 3 - 11y + 1/4

Combining like terms:
-11.5x = 3 - 44y + 1
-11.5x = 4 - 44y

Step 8: Divide both sides of the equation by -11.5 to solve for x:
x = (4 - 44y) / -11.5
Simplify further if possible.

Step 9: Now you have expressions for x and y. To determine whether the system has a unique solution, no solution, or infinite solutions, compare the coefficients of x and y.

The system will have:
- A unique solution if the coefficients of x and y are not equal.
- No solution if the coefficients of x and y are equal, but the constant terms are not equal.
- Infinite solutions if the coefficients of x and y are equal, and the constant terms are equal.

To determine the above, compare the coefficients of x and y and the constant terms in the expressions you found for x and y.

In this case, there are different coefficients for x (-11.5) and y (-1/2), and there are no constant terms in the expressions for x and y. Hence, the system of equations has a unique solution.

Therefore, the given system of equations has a unique solution.