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=(D_(y))/(D)`

Applying the concept:

`image`

`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`

`image`

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}`