Exam 15: Systems of Equations: Matrices and Determinants

Solve the system. $\left(\begin{array}{rl}3 x+3 y-3 z & =-12 \\5 y+4 z & =17 \\3 y-5 z & =-12\end{array}\right)$

Solve the system. $\left( \begin{array} { r l l } 5 x &+ &3 y &-& 4 z & = &24 \\&&x & -& 2 z & =& 6 \\&&3 x &+ &4 z & = & - 2\end{array} \right)$

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l } 4 x ^ { 2 } + 3 y ^ { 2 } & = 24 \\y ^ { 2 } - 4 x ^ { 2 } & = 12\end{array} \right)$ Express your answer as an ordered pair. If there is more than one solution, separate your answers with a comma.

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $\left[ \begin{array} { l l l l | l } 1 & 0 & 0 & 7 & 4 \\0 & 1 & 0 & 0 & 7 \\0 & 0 & 1 & 9 & 5 \\0 & 0 & 0 & 0 & 0\end{array} \right]$ If a system is inconsistent, so indicate.

Solve the system by the substitution or elimination method. $\left( \begin{array} { l l l } y & =& - x ^ { 2 }& +& 5 \\x &+& y &= &6\end{array} \right)$ Express your answer as an ordered pair. If there is more than one solution, separate your answers with a comma.

Use a matrix approach to solve the system. $\left( \begin{array} { c } - 5 x + y + 2 z = 21 \\6 x + 8 y - z = - 72 \\x + 2 y + z = - 9\end{array} \right)$ If a system is inconsistent, so indicate. In those cases enter inconsistent . Otherwise, enter your answer in the form ( x , y ).

Solve the system by the substitution or elimination method. $\left( \begin{array} { l } y = - x ^ { 2 } + 38 \\y = x ^ { 2 } + 6\end{array} \right)$

The elimination-by-addition method and the graphing method can be used to obtain exact solutions for any system of two linear equations in two unknowns.

Solve the system by using the elimination-by-addition method. $\left( \begin{array} { l } 3 x + 6 y = 3 \\5 x - 6 y = 1\end{array} \right)$

If $D = 0$ , then the system of equations is either consistent or the equations are dependent.

If two rows (or columns) of a square matrix A are identical, then $| A | = 1$ .

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { lll } y &=& 3 x \\0.31 x &+& 0.09 y &= &232\end{array} \right)$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { l l } 3 & 2 \\1 & 7\end{array} \right|$ Please enter your answer as a number.

Michelle can enter a small business as a full partner and receive a salary of $40,000 a year and 15% of the year's profit, or she can be sales manager for a salary of $75,000 plus 5% of the year's profit. What must the year's profit be for her total earnings to be the same whether she is a full partner or a sales manager?

Solve each system of equations by the substitution or elimination method. Match each system of equations with the corresponding answer. - $( 8 , - 96 )$

Use Cramer s rule to find the solution set for the system. $\left( \begin{array} { r l l } 4 x - 4 y & = 0 \\y & = 5\end{array} \right)$

Match each step with step-by-step description of how you would solve the system. $\left( \begin{array} { c } 2 x - y + 3 z = 24 \\x - 2 y - z = 1 \\3 x + 5 y + 8 z = 47\end{array} \right)$ -Finding D , D_x , D_y , D_z . D = 22, D_x = 88, D_y = -22, D_z = 110

The matrix is in reduced echelon form. $\left. \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 0\end{array} \right] \quad \begin{array} { c } - 14 \\- 2 \\0\end{array} \right]$

Use Cramer s rule to find the solution set for the system. $\left( \begin{array} { r l } - x - y + 6 z & = 8 \\- 5 x + y + 13 z & = 19 \\6 x + 2 y - 11 z & = 7\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

One day last summer, Jim went kayaking on the Little Susitna River in Alaska. Paddling upstream against the current, he traveled 24 miles in 3 hours. Then he turned around and paddled twice as fast downstream and, with the help of the current, traveled 25 miles in 1 hour. Find the rate of the current.