Exam 3: Systems of Equations

When solving a system of two linear equations by the graphing method, we look for the point of __________ of the two lines.

Matrices were used to solve a system of two linear equations. The final matrix is shown $\left[ \begin{array} { c c : c } 2 & - 2 & 1 \\0 & 0 & - 8\end{array} \right]$ . Which of the following statements is true?

Elementary __________ operations are used to produce equivalent matrices that lead to the solution of a system.

Erin has a total of 64 coins consisting of nickels, dimes, and quarters. The value of the coins is $9.55. There are six more nickels and dimes than quarters. Find the number of nickels.

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x + y + 2 z = 13 \\x + 2 y + z = 11 \\2 x + y + z = 12\end{array} \right.$

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. $\left\{ \begin{array} { l } 4 x + 5 y = 12 \\x - 3 = - \frac { 5 y } { 4 }\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } x + \frac { 1 } { 3 } y + z = 12 \\\frac { 1 } { 3 } x - y + \frac { 1 } { 2 } z = - 2 \\x + \frac { 1 } { 2 } y - \frac { 1 } { 2 } z = 7\end{array} \right.$

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

Determine whether the given ordered triple is a solution of given system. $( 1 , - 5,2 ) , \left\{ \begin{array} { l } 2 x + 2 y + 3 z = - 2 \\3 x + y - z = - 4 \\x + y + 2 z = 0\end{array} \right.$

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. $\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 13 \\x + y - 4 z = - 7\end{array} \right.$

Evaluate the determinant. $\left| \begin{array} { r r r } 1 & - 2 & 5 \\- 2 & 1 & 1 \\- 5 & - 2 & 1\end{array} \right|$

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. $\left\{ \begin{array} { l } x + 2 y + 2 z = 6 \\2 x + y + 2 z = 8 \\2 x + 2 y + z = - 4\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 6 a - 3 b = 1 \\5 a - 8 c = 1 \\2 b - 6 c = 0\end{array} \right.$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } a + b + c = 180 \\\frac { a } { 4 } + \frac { b } { 2 } + \frac { c } { 3 } = 60 \\2 b + 3 c - 190 = 0\end{array} \right.$

If the denominator determinant D for a system of equations is zero, the equations of the system are dependent or the system is __________.

In the triangle, $\angle B$ is $20 ^ { \circ }$ more than $\angle A$ , and $\angle C$ is $20 ^ { \circ }$ less than twice $\angle A$ . Find each angle in the triangle. ( Hint: The sum of the angles in a triangle is $180 ^ { \circ }$ .) $\angle A =$ __________ $0$ $\angle B =$ __________ $∘$ $\angle C =$ __________ $∘$

Evaluate the determinant. $\left| \begin{array} { r r r } 1 & 1 & - 1 \\1 & 1 & 0 \\1 & 0 & 1\end{array} \right|$

Evaluate the determinant. $\left| \begin{array} { r r } - 5 & 2 \\6 & - 4\end{array} \right|$

When three planes intersect in a line, the system will have __________ many solutions.

A beauty shop specializing in permanents has fixed costs of $2,366.40 per month. The owner estimates that the cost for each permanent is $23.60, which covers labor, chemicals, and electricity. If her shop can give as many permanents as she wants at a price of $44 each, how many must be given each month to break even? __________ permanents