solve the system of equations 6x - 3y=-6 9x-3y=-18

Answer 1

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

Let's use the elimination method:

First, we will multiply the first equation by 3 to make the coefficients of y in both equations the same:

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

Now, subtract the second equation from the first equation:

18x - 9y - (9x - 3y) = -18 - (-18)
18x - 9y - 9x + 3y = -18 + 18
9x - 6y = 0
3x - 2y = 0
2y = 3x
y = (3/2)x

Now, we can substitute this expression for y into either of the original equations. Let's substitute it into the first equation:

6x - 3(3/2)x = -6
6x - (9/2)x = -6
(12/2)x - (9/2)x = -6
(3/2)x = -6
x = -4

Now we can substitute the value of x back into y = (3/2)x to find y:

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

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