Question

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

Answer 1

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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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