Solve the system of equations.
6x−3y=−6
9x−3y=−18
To solve the system of equations, we can use the method of substitution.
1) Rearrange the first equation to solve for x in terms of y:
6x - 3y = -6
6x = 3y - 6
x = (3y - 6)/6
x = (y - 2)/2
2) Substitute this expression for x into the second equation:
9x - 3y = -18
9((y - 2)/2) - 3y = -18
(9y - 18)/2 - 3y = -18
9y - 18 - 6y = -36
3y = -18
y = -6
3) Substitute the value of y back into the expression for x:
x = (y - 2)/2
x = (-6 - 2)/2
x = -8/2
x = -4
Therefore, the solution to the system of equations is x = -4 and y = -6.
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the equations.
First, let's rearrange both equations so that the variables line up:
Equation 1: 6x - 3y = -6
Equation 2: 9x - 3y = -18
Notice that both equations have the same coefficients for the variable "y." To eliminate the "y" variable, you can subtract Equation 1 from Equation 2:
(9x - 3y) - (6x - 3y) = -18 - (-6)
This simplifies to:
9x - 3y - 6x + 3y = -18 + 6
The "y" terms cancel out because -3y + 3y = 0y which is equal to 0. The equation then becomes:
9x - 6x = -12
Simplifying further:
3x = -12
Now, divide both sides of the equation by 3 to solve for "x":
3x/3 = -12/3
x = -4
Now that we know the value of "x," we can substitute it back into either of the original equations to find the value of "y." Let's use Equation 1:
6x - 3y = -6
Substituting x = -4:
6(-4) - 3y = -6
-24 - 3y = -6
Next, we will isolate the "y" variable:
-3y = -6 + 24
-3y = 18
Divide both sides of the equation by -3 to solve for "y":
(-3y)/(-3) = 18/(-3)
y = -6
The solutions to the system of equations are x = -4 and y = -6.