Answer: -3x - 6y = -27 (Equation 1)
4x - 2y = -4 (Equation 2)
We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can start by multiplying Equation 2 by 3 to eliminate the y variable:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
Now we can add Equation 1 to Equation 2:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
9x = -39
Simplifying this expression, we get:
x = -39/9 = -13/3
Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
-3x - 6y = -27
-3(-13/3) - 6y = -27
13 + 6y = -27
6y = -40
y = -40/6 = -20/3
Therefore, the solution to the system of equations is x = -13/3 and y = -20/3, or (-13/3, -20/3) in coordinate form.
To check the solution, we can substitute the values of x and y into both equations:
-3(-13/3) - 6(-20/3) = -27
4(-13/3) - 2(-20/3) = -4
Simplifying both expressions, we get:
13 + 40 = 27 (which is true)
-52/3 + 40/3 = -4 (which is also true)
Therefore, the solution is correct.
Explanation: