Exam 3: Systems of Equations

$5 ^ { 3 x } = 6$ is the __________ form of a linear equation.

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 4 x + 4 y = 16 \\- x - y = - 4\end{array} \right.$

Find the y -coordinate of the solution of the following system. $\left\{ \begin{array} { l } x + 7 y - 3 z = - 9 \\2 x - y + z = 6 \\- x + y - z = - 3\end{array} \right.$

Solve the system. To do so, substitute $a + b i$ for $( 7 - 4 i ) - ( 3 + 2 i )$ and $4 - 6 i$ for $\frac { 1 } { y }$ and solve for $\alpha$ and $b$ . Then find $x$ and $y$ using the fact that $a = \frac { 1 } { x }$ and $b = \frac { 1 } { y }$ . $\left\{ \begin{array} { l } \frac { 1 } { x } + \frac { 1 } { y } = \frac { 11 } { 30 } \\\frac { 1 } { x } - \frac { 1 } { y } = \frac { 1 } { 30 }\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } x + y + z = 4 \\x - y + z = 4 \\x - y - z = 2\end{array} \right.$

The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is 9 more than the original number. Find the original number.

Evaluate the determinant: $8 - 4$ 1 -2

The receipts for one showing of a movie were $808 for an audience of 110 people. Children's tickets are $6, general admission is $8, and tickets for seniors are $7. Twice as many general admission tickets as children's tickets were purchased. If x is the number of children's tickets purchased, y is the number of general admissions tickets purchased, and z is the number of senior tickets purchased, write a system of three equations in three variables that models the situation.

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 5 x + 2 y = 0 \\10 x - 4 y = - 4\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x + y + z = 6 \\x + y - z = 0 \\x - y + z = 4\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{aligned}x - 2 y & = 8 \\- 2 x + 4 y & = 16\end{aligned} \right.$

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $a + b i$

The owner of a produce store wanted to mix peanuts selling for $1 per pound, cashews selling for $8 per pound, and Brazil nuts selling for $8 per pound to get 70 pounds of a mixture that would sell for $5 per pound. She used 15 fewer pounds of cashews than peanuts. How many pounds of peanuts did she use?

Solve the following system of equations by any method. $( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )$

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 5 x + 4 y = 12 \\10 x + 8 y = 12\end{array} \right.$

The sum of the digits of a two-digit number is 9. If the digits are reversed the new number is 9 less than the original number. Find the original number.

If two lines are parallel,

Tell whether the ordered pair (1,2) is a solution of the system of equations. $\left\{ \begin{array} { l } 3 x - y = 1 \\y = \frac { 1 } { 2 } x + \frac { 3 } { 2 }\end{array} \right.$

Write the system of equations represented by the augmented matrix. $\left[ \begin{array} { c c c | c } 1 & - 2 & 1 & - 12 \\0 & 1 & 2 & 8 \\0 & 0 & 1 & 4\end{array} \right]$ __________ Use back substitution to find the solution. __________

Evaluate the determinant. $4 \quad - 4$ 78