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. $x=\frac34,y=\frac45$
• D. $x=\frac45,y=\frac34$

Answer: (D)

Verified step by step guidance

1. Start by writing down the given system of equations: \( 10x - 4y = 5 \) and \( 5x - 4y = 1 \).
2. Notice that both equations have the term \(-4y\). To eliminate \(y\), subtract the second equation from the first equation: \((10x - 4y) - (5x - 4y) = 5 - 1\).
3. Simplify the result of the subtraction: \(10x - 5x = 5 - 1\), which simplifies to \(5x = 4\).
4. Solve for \(x\) by dividing both sides of the equation \(5x = 4\) by 5: \(x = \frac{4}{5}\).
5. Substitute \(x = \frac{4}{5}\) back into either original equation to solve for \(y\). For example, using \(5x - 4y = 1\), substitute \(x\) and solve for \(y\).