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Explain Bot To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables by manipulating the equations so that the coefficients of one of the variables are the same.
Let's start by writing down the system of equations:
6x - 3y = -6 ...(Equation 1)
9x - 3y = -18 ...(Equation 2)
Notice that the coefficients of y are already the same (-3) in both equations. Therefore, we can directly subtract Equation 1 from Equation 2 to eliminate y:
(9x - 3y) - (6x - 3y) = -18 - (-6)
9x - 3y - 6x + 3y = -18 + 6
(9x - 6x) + (-3y + 3y) = -12
3x = -12
Now, we can solve for x by dividing both sides of the equation by 3:
3x/3 = -12/3
x = -4
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use Equation 1:
6x - 3y = -6
Substituting x = -4:
6(-4) - 3y = -6
-24 - 3y = -6
To isolate y, we'll add 24 to both sides of the equation:
-24 + 24 - 3y = -6 + 24
-3y = 18
Dividing both sides by -3:
-3y / -3 = 18 / -3
y = -6
Therefore, the solution to the system of equations is x = -4 and y = -6.