Questions: x-4y=4 -x+4y=4

Transcript text: x-4y=4 -x+4y=4

Solution

Solution Steps

To solve the system of linear equations, we can use the method of addition (or elimination) to eliminate one of the variables. By adding the two equations, we can eliminate \( y \) and solve for \( x \). Then, we substitute the value of \( x \) back into one of the original equations to find \( y \).

Step 1: Write Down the System of Equations

We start with the given system of linear equations: \[ \begin{aligned} x - 4y &= 4 \\ -x + 4y &= 4 \end{aligned} \]

Step 2: Add the Equations

To eliminate one of the variables, we add the two equations together: \[ (x - 4y) + (-x + 4y) = 4 + 4 \] Simplifying the left-hand side: \[ x - 4y - x + 4y = 8 \] \[ 0 = 8 \]

Step 3: Analyze the Result

The result \(0 = 8\) is a contradiction, which means that the system of equations has no solution. The lines represented by these equations are parallel and do not intersect.

Final Answer

\(\boxed{\text{No solution}}\)

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