Final answer:
The solution to the system of equations 3x+4y=-2 and 2x-4y=-8 is found by adding the equations to eliminate y, which gives x = -2. Substituting x back into one of the original equations then gives y = 1.
Step-by-step explanation:
The solution to the system of equations given by 3x+4y=-2 and 2x-4y=-8 can be found by either the substitution method or the elimination method. Since the y terms, 4y and -4y, are additive inverses, we can eliminate the y variable by adding the two equations together:
- 3x + 4y = -2
- 2x - 4y = -8
Add the equations: (3x + 4y) + (2x - 4y) = -2 + (-8)
This simplifies to 5x = -10.
Divide both sides by 5 to find x: x = -2.
Now, substituting x = -2 into one of the original equations to find y:
2(-2) - 4y = -8
-4 - 4y = -8
-4y = -4
Multiply both sides by -1/4 to isolate y: y = 1.
The solution to the system of equations is x = -2 and y = 1.