Use the elimination method to solve the following system of linear equations.
$10x-4y=5$
$5x-4y=1$

• A. $x=12,y=16$
• B. $x=16,y=12$
• C. $x=\(\frac\)34,y=\(\frac\)45$
• D. $x=\(\frac\)45,y=\(\frac\)34$

Answer: (D)

Verified step by step guidance

1. Write down the system of equations: \(10x - 4y = 5\) \(5x - 4y = 1\)
2. To use the elimination method, subtract the second equation from the first to eliminate \(y\) because both have the same coefficient \(-4y\): \((10x - 4y) - (5x - 4y) = 5 - 1\)
3. Simplify the subtraction: \(10x - 4y - 5x + 4y = 4\) This reduces to: \(5x = 4\)
4. Solve for \(x\) by dividing both sides by 5: \(x = \frac{4}{5}\)
5. Substitute \(x = \frac{4}{5}\) back into one of the original equations (for example, \(5x - 4y = 1\)) and solve for \(y\): \(5 \left( \frac{4}{5} \right) - 4y = 1\)