Use the elimination method to find a general solution for the given linear​ system, where differentiation is with respect to t.
x prime
equals
3 x minus y
y prime
equals
3 y minus 4 x
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Part 1
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.

To solve the system of linear differential equations using **elimination**, we start with the given system:

\[
x' = 3x - y
\]
\[
y' = 3y - 4x
\]

Our goal is to eliminate \(x\) and solve for \(y\). Let's proceed step-by-step:

---

### Step 1: Differentiate \(x' = 3x - y\) with respect to \(t\)
We want to differentiate both sides to get an expression involving \(x''\) and eliminate \(x\):

\[
x'' = 3x' - y'
\]

Using the second equation \(y' = 3y - 4x\), substitute \(y'\) into the above equation:

\[
x'' = 3x' - (3y - 4x)
\]
\[
x'' = 3x' - 3y + 4x
\tag{1}
\]

---

### Step 2: Substitute \(x' = 3x - y\) into the expression
We substitute \(y = 3x - x'\) to solve .



Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.
x' = 3x - y
y' = 3y - 4x

Learn how to solve a system of linear differential equations using the elimination method. This step-by-step guide helps you eliminate variables and solve for y in a system involving x' = 3x - y and y' = 3y - 4x. Ideal for undergraduate students studying calculus or differential equations.

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