General Idea:
The Cramer's rule can be used to find the value of y.
For a system of equation of the form:
[tex] ax+by+cz=j [/tex]
[tex] dx+ey+fz=k [/tex]
[tex] gx+hy+iz=l [/tex]
Determinant [tex] D =\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right] [/tex]
[tex] D_{y} =\left[\begin{array}{ccc}a&j&c\\d&k&f\\g&l&i\end{array}\right] [/tex]
[tex] y=\frac{D_{y}}{D} [/tex]
Applying the concept:
[tex] x+2x-2z=3
3x-y+z=16
x+z=7 [/tex]
[tex] D=\left[\begin{array}{ccc}1&2&-2\\3&-1&1\\1&0&1\end{array}\right] \\D=1(-1-0)-2(3-1)-2(0+1)\\D=-1-4-2\\ D=-7 [/tex]
[tex] D_y=\left[\begin{array}{ccc}1&3&-2\\3&16&1\\1&7&1\end{array}\right] \\ D_y=1(16-7)-3(3-1)-2(21-16)\\
D_y=9-6-10 \\D_y=-7 [/tex]
Conclusion:
The expression which gives the y-coordinate of the solution of the system is option D.
[tex] OptionD=\frac{\left[\begin{array}{ccc}1&3&-2\\3&16&1\\1&7&1\end{array}\right] }{-7} [/tex]
