Answer:
Let's solve the system of equations algebraically:
4x - 2y = 8
2x - 4y = 4
We can simplify both equations by dividing them by their respective coefficients to make it easier to work with:
Divide equation (1) by 2:
(4x - 2y)/2 = 8/2
2x - y = 4
Divide equation (2) by 2:
(2x - 4y)/2 = 4/2
x - 2y = 2
Now, we have the simplified system of equations:
2x - y = 4
x - 2y = 2
Let's use the method of substitution to solve this system. We'll solve equation (2) for x:
x = 2y + 2
Now, substitute this expression for x into equation (1):
2x - y = 4
2(2y + 2) - y = 4
Simplify and solve for y:
4y + 4 - y = 4
3y + 4 = 4
Subtract 4 from both sides:
3y = 0
Now, divide by 3:
y = 0
Now that we have the value of y, substitute it back into the equation x = 2y + 2:
x = 2(0) + 2
x = 2
So, the solution to the system of equations is (x, y) = (2, 0).
The correct answer is C. (2, 0).
Explanation:
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