Use substitution to solve the following system of linear equations.
$4x+y=1$
$x-y=4$

• A. $\left(-1,3\right)$
• B. $\left(-3,1\right)$
• C. $\left(3,-1\right)$
• D. $\left(1,-3\right)$

Answer: (D)

Verified step by step guidance

1. Start by identifying the two equations in the system: \(4x + y = 1\) and \(x - y = 4\).
2. Choose one of the equations to solve for one variable. Let's solve the second equation \(x - y = 4\) for \(x\). Rearrange it to get \(x = y + 4\).
3. Substitute \(x = y + 4\) into the first equation \(4x + y = 1\). This gives \(4(y + 4) + y = 1\).
4. Simplify the equation \(4(y + 4) + y = 1\) to find the value of \(y\). Distribute the 4 to get \(4y + 16 + y = 1\), then combine like terms to get \(5y + 16 = 1\).
5. Solve the equation \(5y + 16 = 1\) for \(y\). Once you find \(y\), substitute it back into \(x = y + 4\) to find \(x\).