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

Question

asked Jan 21, 2019 11.4k views

1 Answer

Doree · Answer 1 · 2019-01-26T23:10:53+0000

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:

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

Conclusion:

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

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