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 with the given system of equations: \$4x + y = 1\( and \)x - y = 4$.
2. From the second equation, solve for \(x\) in terms of \(y\): \(x = y + 4\).
3. Substitute the expression for \(x\) from step 2 into the first equation: \$4(y + 4) + y = 1$.
4. Simplify and solve the resulting equation for \(y\): \$4y + 16 + y = 1\( which simplifies to \)5y + 16 = 1$.
5. Once you find \(y\), substitute it back into \(x = y + 4\) to find the value of \(x\).