91Ó°ÊÓ

Solve the given linear system. State whether the system is consistent, with independent or dependent equations, or whether it is inconsistent. $$ \left\\{\begin{array}{l} x-y=2 \\ x+y=1 \end{array}\right. $$

Write out the appropriate form of the partial fraction decomposition of the given rational expression. Do not evaluate the coefficients. $$ \frac{2 x^{3}-x}{\left(x^{2}+1\right)^{2}} $$

Determine graphically whether the given nonlinear system has any real solutions. $$ \left\\{\begin{array}{l} y-x^{2}=0 \\ x^{2}-y^{2}=4 \end{array}\right. $$

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

Graph the given inequality. \(x^{2}+\frac{1}{4} y^{2}<1\)

Write out the appropriate form of the partial fraction decomposition of the given rational expression. Do not evaluate the coefficients. $$ \frac{-x^{2}+3 x+7}{\left(x^{2}+x-2\right)\left(x^{2}+x+1\right)^{3}} $$

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

Determine graphically whether the given nonlinear system has any real solutions. $$ \left\\{\begin{array}{l} y=-x^{2}+2 x \\ (x-1)^{2}+y^{2}=1 \end{array}\right. $$

Evaluate the given determinant. In Problem 10 , assume that \(a \neq 0, b \neq 0\). $$ \left|\begin{array}{rr} 3 & -4 \\ 5 & 6 \end{array}\right| $$

Determine graphically whether the given nonlinear system has any real solutions. $$ \left\\{\begin{array}{l} y=\sqrt{x} \\ y=2^{-x} \end{array}\right. $$