Final answer:
The solution to the system of equations is x = 0.8 and y = -0.125, found through the elimination method by multiplying the second equation by 2 and then adding to the first to eliminate y.
Step-by-step explanation:
The solution to the system of equations 10x + 16y = 6 and 5x - 8y = 5 can be found using either substitution or elimination methods. To use elimination, we can multiply the second equation by 2 to make the coefficients of y in both equations equal with opposite signs:
- 10x + 16y = 6
- (5x - 8y = 5) * 2 ⇒ 10x - 16y = 10
Add the two equations to eliminate y:
- 10x + 16y + 10x - 16y = 6 + 10
- 20x = 16
- x = 16 / 20
- x = 0.8
Now substitute x = 0.8 into the first equation to solve for y:
- 10(0.8) + 16y = 6
- 8 + 16y = 6
- 16y = 6 - 8
- 16y = -2
- y = -2 / 16
- y = -0.125
The solution to the system of equations is x = 0.8 and y = -0.125.