Exam 3: Systems of Equations

Solve using elimination: $\left\{ \begin{array} { l } x + 3 y + z = 8 \\3 x - 6 y + z = - 8 \\4 x - y - 8 z = - 6\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 12 \\8 x + 6 y = 12\end{array} \right.$

Which matrix shown below indicates that the equations of its associated system are dependent? $\text { a. } \left[ \begin{array} { c c | c } 1 & 5 & - 7 \\0 & 0 & 0\end{array} \right]$ $\text { b. } \left[ \begin{array} { r r | r } 1 & 5 & - 7 \\0 & 4 & 0\end{array} \right]$ $\text { c. } \left[ \begin{array} { l l | r } 1 & 5 & - 7 \\0 & 0 & 5\end{array} \right]$ Enter a, b or c . __________

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 x + y - 3 z = - 10 \\3 x - y + 2 z = - 3 \\- 2 x - y - z = - 2\end{array} \right.$

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? __________ Are the equations dependent or independent? __________

Use the method of elimination to find the y -coordinate of the solution of the following system of equations. $i ^ { 28 }$

Solve the system by graphing. $\left\{ \begin{array} { l } 2 x + y = 0 \\x - 2 y = - 15\end{array} \right.$

Solve the system by any method, if possible. ${ } ^ { 227 } \mathrm { Th }$

Use matrices to solve $\left\{ \begin{array} { l } 12 x ^ { 2 } - 2 y ^ { 2 } + 8 z ^ { 2 } = 3 \\4 x ^ { 2 } + 7 y ^ { 2 } + 2 z ^ { 2 } = \frac { 17 } { 2 } \\2 x ^ { 2 } + 7 y ^ { 2 } - 4 z ^ { 2 } = \frac { 13 } { 2 }\end{array} \right.$

Two angles are complementary. The measure of the larger angle is 55? less than twice the measure of the smaller angle. If x measures the smaller angle and y measures the larger angle, write a system of two equations in two unknowns that would model the situation.

Solve the system by substitution, if possible. If the system is inconsistent or if the equations are dependent, so indicate. $3 + 5 i$

The receipts for one showing of a movie were $775 for an audience of 150 people. The ticket prices were $7.00 for adults and $4.50 for children under age 12 and adults over age 65. How many adult tickets were sold? ________ adult tickets

Evaluate the determinant. $\left| \begin{array} { r r r } - 1 & 3 & 1 \\- 3 & 1 & - 5 \\1 & 1 & 1\end{array} \right|$

A matrix that represents the equations of a system is called a(n) __________ matrix.

Represent the system of equations using an augmented matrix. $\left\{ \begin{array} { l } 3 x + 2 y = 5 \\x - y = - 5\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } x + y = 8 \\x - y = 2\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } b + 2 c = 12 - a \\a + c = 12 - 2 b \\2 a + b + c = 12\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 3 x + y - 3 z = 2 \\x - 2 y + 4 z = 9 \\x + y + z = 12\end{array} \right.$

Solve: $\left\{ \begin{array} { l } 7 a + 3 b - 8 c + 2 d = - 4 \\5 a - 8 b + 5 c - 4 d = 15 \\5 a - 4 b + 8 c + 7 d = 16 \\7 a + b - 4 c + 4 d = 2\end{array} \right.$

Solve the system by graphing. $\left\{ \begin{array} { l } 2 x + y = 2 \\x + y = 0\end{array} \right.$