Question

Which expression gives the y-coordinate of the solution of the system? 3915518_Eqn011.gif

Answer 1

General Idea:

The Cramer's rule can be used to find the value of y.

For a system of equation of the form:

$ax+by+cz=j$

$dx+ey+fz=k$

$gx+hy+iz=l$

Determinant $D =\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]$

$D_{y} =\left[\begin{array}{ccc}a&j&c\\d&k&f\\g&l&i\end{array}\right]$

$y=\frac{D_{y}}{D}$

Applying the concept:

$x+2x-2z=3\\3x-y+z=16\\x+z=7$

$D=\left[\begin{array}{ccc}1&2&-2\\3&-1&1\\1&0&1\end{array}\right] \\D=1(-1-0)-2(3-1)-2(0+1)\\D=-1-4-2\\ D=-7$

$D_y=\left[\begin{array}{ccc}1&3&-2\\3&16&1\\1&7&1\end{array}\right] \\ D_y=1(16-7)-3(3-1)-2(21-16)\\ D_y=9-6-10 \\D_y=-7$

Conclusion:

The expression which gives the y-coordinate of the solution of the system is option D.

$OptionD=\frac{\left[\begin{array}{ccc}1&3&-2\\3&16&1\\1&7&1\end{array}\right] }{-7}$