91Ó°ÊÓ

In Problems \(11-46,\) solve the given nonlinear system. $$ \left\\{\begin{array}{l} y=x \\ y^{2}=x+2 \end{array}\right. $$

Evaluate the given determinant. In Problem 10 , assume that \(a \neq 0, b \neq 0\). $$ \left|\begin{array}{rrr} -3 & 4 & 1 \\ 2 & -6 & 1 \\ 6 & 8 & -4 \end{array}\right| $$

Solve the given linear system. State whether the system is consistent, with independent or dependent equations, or whether it is inconsistent. $$ \left\\{\begin{array}{c} x+y-z=0 \\ x-y+z=2 \\ 2 x+y-4 z=-8 \end{array}\right. $$

Graph the given inequality. \(y \geq|x+2|\)

Find the partial fraction decomposition of the given rational expression. $$ \frac{-5 x+18}{x^{2}+2 x-63} $$

Evaluate the given determinant. In Problem 10 , assume that \(a \neq 0, b \neq 0\). $$ \left|\begin{array}{rrr} 6 & 2 & 1 \\ 0 & 3 & -4 \\ 1 & 0 & 2 \end{array}\right| $$

Solve the given linear system. State whether the system is consistent, with independent or dependent equations, or whether it is inconsistent. $$ \left\\{\begin{array}{l} x+y+z=8 \\ x-2 y+z=4 \\ x+y-z=-4 \end{array}\right. $$

Solve the given nonlinear system. $$ \left\\{\begin{array}{l} y=3 x \\ x^{2}+y^{2}=4 \end{array}\right. $$

Evaluate the given determinant. In Problem 10 , assume that \(a \neq 0, b \neq 0\). $$ \left|\begin{array}{rrr} 4 & 6 & 1 \\ 3 & 2 & 3 \\ 0 & -1 & 7 \end{array}\right| $$

$$ \left\\{\begin{array}{l} 2 x+6 y+z=-2 \\ 3 x+4 y-z=2 \\ 5 x-2 y-2 z=0 \end{array}\right. $$