Final answer:
By using the elimination method, we determined the solution to the system of equations 2x-8y=10 and 3x+9y=20. The solution is x=125/21 and y=5/21.
Step-by-step explanation:
To solve the system of equations 2x-8y=10 and 3x+9y=20 using the elimination method, we need to manipulate the equations to eliminate one variable.
This can be achieved by making the coefficients of either x or y the same in both equations, then adding or subtracting one equation from the other.
Let's multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same:
- (3)(2x - 8y) = (3)(10) → 6x - 24y = 30
- (2)(3x + 9y) = (2)(20) → 6x + 18y = 40
Now, subtract the second modified equation from the first:
- 6x - 24y - (6x + 18y) = 30 - 40
- -42y = -10
Solving for y, we get:
y = -10 / -42 → y = 5/21
Substitute y = 5/21 into either original equation to find x. Let's use the first equation:
- 2x - 8(5/21) = 10
- 2x - 40/21 = 10
- 2x = 10 + 40/21
- 2x = 250/21
- x = 125/21
So, the solution to the system of equations is x = 125/21 and y = 5/21.