Final answer:
To solve the system of equations 3x-2y=-2 and 4x-3y=-4 by elimination, multiply the equations by appropriate values to make the coefficients equal and then eliminate a variable. Finally, solve for the remaining variable.
Step-by-step explanation:
The given system of equations is:
3x - 2y = -2 (Equation 1)
4x - 3y = -4 (Equation 2)
To solve the system of equations by elimination, we need to eliminate one variable by multiplying one or both equations by appropriate values that will result in the coefficients of a variable being equal with opposite signs.
Step 1: Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x equal:
9x - 6y = -6 (Equation 3)
8x - 6y = -8 (Equation 4)
Step 2: Subtract Equation 4 from Equation 3:
(9x - 6y) - (8x - 6y) = (-6) - (-8)
x = 2
Step 3: Substitute the value of x into one of the original equations (Equation 1 or Equation 2) to solve for y:
3(2) - 2y = -2
6 - 2y = -2
-2y = -8
y = 4
Therefore, the solution to the system of equations is x = 2 and y = 4.