Solve using the elimination method.

-3x+6y=-3
-6x+4y=-10

multiply the top by 2 and subtract

-6x + 12y = -6
-6x + 4y = -10

8y = 4
y = 1/2
so,
x = 2

To solve this system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.

First, let's choose a variable to eliminate. In this case, we will need to eliminate the variable "x". To do this, we need to multiply one or both of the equations by a constant so that the coefficients of "x" will be the same or multiples of each other.

Let's start by multiplying the first equation by 2 and the second equation by 3:

2*(-3x + 6y) = 2*(-3)
3*(-6x + 4y) = 3*(-10)

This simplifies the equations to:

-6x + 12y = -6
-18x + 12y = -30

Now, we can subtract the second equation from the first equation to eliminate "x":

(-6x + 12y) - (-18x + 12y) = (-6) - (-30)

Simplifying further:

-6x + 12y + 18x - 12y = -6 + 30
12x = 24

Dividing both sides of the equation by 12:

12x/12 = 24/12
x = 2

Now that we have found the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use the first equation:

-3x + 6y = -3
-3(2) + 6y = -3
-6 + 6y = -3
6y = -3 + 6
6y = 3

Dividing both sides of the equation by 6:

6y/6 = 3/6
y = 1/2

Therefore, the solution to the system of equations -3x + 6y = -3 and -6x + 4y = -10 is x = 2 and y = 1/2.