Solve the system of equations

Question

6x-3y=-6
9x-3y=-18

Answer 1

To solve this system of equations, we will manipulate one of the equations to make it easier to eliminate one of the variables. Let's multiply the first equation by 3:

18x - 9y = -18
9x - 3y = -18

Now, we can subtract the second equation from the first:

18x - 9y - 9x + 3y = (-18) - (-18)
9x - 6y = 0
Divide by 3 to get the simplest form:
3x - 2y = 0

Now we can solve this simplified equation along with one of the original equations to find the values of x and y. Let's use the first original equation:

6x - 3y = -6

Let's solve for x in terms of y:
6x = 3y - 6
x = (3y - 6) / 6
x = (y - 2) / 2

Now, we can substitute this x expression into the simplified equation:

3((y-2)/2) - 2y = 0
(3y - 6)/2 - 2y = 0
3y - 6 - 4y = 0
-y - 6 = 0
-y = 6
y = -6

Now that we have found the value of y, we can substitute it back into our x equation to solve for x:

x = (-6 - 2) / 2
x = -8 / 2
x = -4

Therefore, the solution to the system of equations is:
x = -4
y = -6