Explicação passo a passo:
[tex]3\cdot\left[\begin{array}{cc}x&2\\-z&1\end{array}\right]-\left[\begin{array}{cc}y&6\\5&y\end{array}\right]=\left[\begin{array}{cc}7&0\\10&4\end{array}\right][/tex]
Logo:
[tex]\left[\begin{array}{cc}3x&6\\-3z&3\end{array}\right]-\left[\begin{array}{cc}y&6\\5&y\end{array}\right]=\left[\begin{array}{cc}7&0\\10&4\end{array}\right]\\\left[\begin{array}{cc}3x-y&6-6\\-3z-5&3-y\end{array}\right]=\left[\begin{array}{cc}7&0\\10&4\end{array}\right][/tex]
Transformando em um sistema de equações:
[tex]\begin{cases} 3x-y=7\quad\quad(I)\\-3z-5=10\quad\quad (II)\\3-y=4 \quad\quad(III) \end{cases}[/tex]
Resolvendo a equação [tex](II)[/tex]:
[tex]-3z-5=10\\-3z=15\\z=-5[/tex]
Resolvendo a equação [tex](III)[/tex]:
[tex]3-y=4\\-y=1\\y=-1[/tex]
Substituindo o valor de [tex]y[/tex] em [tex](I)[/tex]:
[tex]3x-y=7\\3x-(-1)=7\\3x+1=7\\3x=6\\x=2[/tex]
Portanto: [tex]x=2,y=-1,z=-5[/tex]
