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Which system of equations is represented by this matrix?
[2 -1 | -4]
[3 -2 | -6]

User Liondancer
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The given system of equations is:


\displaystyle\sf \begin{align}2x - y &= -4\\3x - 2y &= -6\end{align}

To solve this system, we can use the method of elimination or substitution. Let's use the method of elimination:

First, we'll multiply the first equation by 2 to make the coefficients of
\displaystyle\sf y in both equations equal:


\displaystyle\sf \begin{align}4x - 2y &= -8\\3x - 2y &= -6\end{align}

Now, we can subtract the second equation from the first equation to eliminate the variable
\displaystyle\sf y:


\displaystyle\sf (4x - 2y) - (3x - 2y) = -8 - (-6)

Simplifying the expression:


\displaystyle\sf x = -2

Now that we have found the value of
\displaystyle\sf x, we can substitute it back into either of the original equations to solve for
\displaystyle\sf y. Let's substitute it into the first equation:


\displaystyle\sf 2(-2) - y = -4

Simplifying the expression:


\displaystyle\sf -4 - y = -4

Solving for
\displaystyle\sf y:


\displaystyle\sf -y = 0


\displaystyle\sf y = 0

Hence, the solution to the system of equations is
\displaystyle\sf x = -2 and
\displaystyle\sf y = 0.


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User Emersonthis
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