Final answer:
By using the elimination method, the x variable was cancelled, leading to finding the value of y, which was then substituted back into an equation to find x, resulting in the solution (x, y) = (-8, 12).
Step-by-step explanation:
To solve the system of equations 5x + 4y = 8 and -5x - 3y = 4 using the elimination method, we look to eliminate one of the variables by adding or subtracting the equations. When we add the two equations together, we eliminate the x variable, since 5x and -5x cancel each other out:
- 5x + 4y = 8
- -5x - 3y = 4
- Add the two equations: (5x - 5x) + (4y - 3y) = 8 + 4
- This simplifies to y = 12
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
- 5x + 4(12) = 8
- 5x + 48 = 8
- 5x = 8 - 48
- 5x = -40
- x = -8
We should always check our answer to ensure it's reasonable by substituting x and y back into the original equations. After checking, we confirm that the solution is correct:
- 5(-8) + 4(12) = 8
- -5(-8) - 3(12) = 4
Therefore, the solution to the system of equations is (x, y) = (-8, 12).