What is the \( x \)-value in the solution to this system of linear equations? \( \begin{array}{l}2 x-y=11 \\ x+3 y=-5 \\ -3 \\ -1 \\ 2 \\ 4\end{array} \)
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To solve the system of equations, we'll use substitution or elimination. Let’s work with the equations \( 2x - y = 11 \) and \( x + 3y = -5 \). From the first equation, we can express \( y \) in terms of \( x \): 1. Rearranging gives us \( y = 2x - 11 \). 2. Substituting this expression for \( y \) into the second equation \( x + 3(2x - 11) = -5 \): \[ x + 6x - 33 = -5 \implies 7x - 33 = -5 \implies 7x = 28 \implies x = 4. \] Therefore, the \( x \)-value in the solution to this system of equations is \( 4 \). Now, let’s wrap up with some fun facts! The elimination method can be thought of like cooking; just like you combine ingredients to get a delicious dish, you combine equations to find an answer! And did you know? The concept of solving systems of equations dates back to Chinese mathematics in the 2nd century AD! It's fascinating how these techniques have evolved into the algebra we learn today.