91Ó°ÊÓ

\(3-8=\) Use the substitution method to find all solutions of the system of equations. $$ \left\\{\begin{aligned} x+y^{2} &=0 \\ 2 x+5 y^{2} &=75 \end{aligned}\right. $$

\(5-8\) Use the substitution method to find all solutions of the system of equations. $$ \left\\{\begin{array}{c}{x-y=2} \\ {2 x+3 y=9}\end{array}\right. $$

\(7-12=\) Use back-substitution to solve the triangular system. $$ \left\\{\begin{aligned} x+y-3 z &=8 \\ y-3 z &=5 \\ z &=-1 \end{aligned}\right. $$

\(3-12\) . Write the form of the partial fraction decomposition of the function (as in Example 4 ). Do not determine the numerical values of the coefficients. $$ \frac{1}{x^{4}-1} $$

\(5-8\) Use the substitution method to find all solutions of the system of equations. $$ \left\\{\begin{array}{l}{2 x+y=7} \\ {x+2 y=2}\end{array}\right. $$

Perform the matrix operation, or if it is impossible, explain why. $$ \left[\begin{array}{lll}{0} & {1} & {1} \\ {1} & {1} & {0}\end{array}\right]-\left[\begin{array}{lll}{2} & {1} & {-1} \\ {1} & {3} & {-2}\end{array}\right] $$

\(3-8=\) Use the substitution method to find all solutions of the system of equations. $$ \left\\{\begin{array}{c}{x^{2}-y=1} \\ {2 x^{2}+3 y=17}\end{array}\right. $$

State the dimension of the matrix. $$ \left[\begin{array}{r}{-3} \\ {0} \\ {1}\end{array}\right] $$

Find the determinant of the matrix, if it exists. $$ \left[\begin{array}{rr}{-2} & {1} \\ {3} & {-2}\end{array}\right] $$

\(9-14\) . Use the elimination method to find all solutions of the system of equations. $$ \left\\{\begin{array}{l}{x^{2}-2 y=1} \\ {x^{2}+5 y=29}\end{array}\right. $$