6x-3y=18
-3x-9y=-93
To solve this system of equations, you can use the method of substitution or elimination.
Let's use the method of substitution:
First, solve one equation for one variable in terms of the other.
From the first equation, solve for x:
6x - 3y = 18
6x = 18 + 3y
x = (18 + 3y)/6
Now, substitute this expression for x into the second equation:
-3x - 9y = -93
-3((18 + 3y)/6) - 9y = -93
Multiply both sides of the equation by 6 to get rid of the fraction:
-3(18 + 3y) - 54y = -93 * 6
-54 - 9y - 54y = -558
Combine like terms:
-63y - 54 = -558
-63y = -558 + 54
-63y = -504
Divide both sides of the equation by -63 to solve for y:
y = -504 / -63
y = 8
Now, substitute this value for y back into the first equation to solve for x:
6x - 3y = 18
6x - 3(8) = 18
6x - 24 = 18
6x = 18 + 24
6x = 42
x = 42 / 6
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 8.