Final answer:
The solution to the system of equations 8x - 2y = 0 and -6x + 14y = 50 is x = 1, y = 4. This solution is found using the elimination method. None of the given options correctly matches this solution.
Step-by-step explanation:
The solution to the system of equations 8x − 2y = 0 and −6x + 14y = 50 can be found by using either the substitution method or the elimination method. To solve these linear equations, we will use the elimination method by multiplying the first equation by 3 and the second equation by 2 to eliminate x when we add them together:
- 24x − 6y = 0 (equation 1 multiplied by 3)
- −12x + 28y = 100 (equation 2 multiplied by 2)
Add the two equations:
- (24x + −12x) + (−6y + 28y) = 0 + 100
- 12x + 22y = 100
Divide every term by 2:
Now we solve for y using the first equation:
Substitute y = 4x into 6x + 11y = 50:
- 6x + 11(4x) = 50
- 6x + 44x = 50
- 50x = 50
- x = 1
Substitute x = 1 into y = 4x:
The solution to the system of equations is x = 1, y = 4. None of the given options a) x = 4, y = 16 b) x = -2, y = 10 c) x = 6, y = 25 d) x = -4, y = -14 is correct. The correct answer is not provided in the given options.