Answer:
-11
Step-by-step explanation:
The given system of equations solved by matrix method is to arrange all coefficients into a matrix, and then making zeros in specific columns and rows, until we get an equation with just one variable.
[tex]\left \{ {{y=3-\frac{1}{2}x } \atop {3x+4y=1}} \right.[/tex]
[tex]\left \{ {{\frac{1}{2}x+ y=3} \atop {3x+4y=1}} \right.[/tex]
In matrix arrangement:
[tex]\left[\begin{array}{ccc}\frac{1}{2} &1&3\\3&4&1\end{array}\right] \\[/tex]
Multiplying by 4 the first row and then subtracting with the second row, we have:
[tex]\left[\begin{array}{ccc}-1 &0&11\\3&4&1\end{array}\right][/tex]
From the firs row, we find that:
[tex]-x+0y=11\\x=-11[/tex]
Therefore, the right answer is -11.
