Exam 3: Systems of Equations

$\left| \begin{array} { c c c } x & y & 1 \\A & - 1 & 1 \\3 & 2 & 1\end{array} \right| = 0$ represents the equation of a line. Find the value of B so that the line passes through the point (-7,12) .

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. $\left\{ \begin{array} { l } 4 x + 3 y = 0 \\8 x - 6 y = - 4\end{array} \right.$

A student is solving the system $10$ by elimination. Which of the following systems is the result if the student wants to eliminate y ?

Solve the system by graphing. $\left\{ \begin{array} { l } y = 4 \\x = 5\end{array} \right.$

In the system $\left\{ \begin{array} { l } x - y + z = 4 \\x + 2 y - z = - 1 \\x + y - 5 z = - 4\end{array} \right.$ , equations 1 and 2 were added to eliminate z . Then equation 2 was multiplied by 5 and added to equation 3 to eliminate z . Which of the following systems of equations would be the result?

How many pounds of each candy shown in the illustration must be mixed to obtain 64 pounds of candy that would be worth $4 per pound? Gummy Bears: __________ lb Jelly Beans: __________ lb

Determine whether the given ordered triple is a solution of given system. $( 7,1,1 ) , \left\{ \begin{array} { l } x - y + z = 7 \\2 x + y - z = 14 \\2 x - 3 y + z = 12\end{array} \right.$

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

Solve the system by elimination if possible. $\log _ { 3 } ( x - 5 ) + \log _ { 3 } ( x + 3 ) = \log _ { 3 } 20$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 2 a + 3 b - 2 c = 18 \\5 a - 6 b + c = 9 \\4 b - 2 c - 14 = 0\end{array} \right.$

Find a cubic equation of the form $y = a x ^ { 3 } + b x ^ { 2 } + c x + d$ passing through the points $( - 2,38 ) , ( - 1,3 ) , ( 1 , - 13 ) , \text { and } ( 2 , - 30 )$ .

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

Use the graphs in the illustration to solve the equation. $- 3 x + 9 = x + 1$

$\left| \begin{array} { l l } a _ { 2 } & c _ { 2 } \\a _ { 3 } & c _ { 3 }\end{array} \right|$ is the minor of what element in $\left| \begin{array} { l l l } a _ { 1 } & b _ { 2 } & c _ { 1 } \\a _ { 2 } & b _ { 2 } & c _ { 2 } \\a _ { 3 } & b _ { 3 } & c _ { 3 }\end{array} \right|$ ?

Tell whether the ordered pair (3,3) is a solution of the system of equations. $\left\{ \begin{array} { l } 5 x - y = 12 \\y = \frac { 1 } { 2 } x + \frac { 3 } { 2 }\end{array} \right.$

An artist makes three types of ceramic statues at a monthly cost of $655 for 180 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue? __________ expensive, __________ middle-priced, __________ inexpensive

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 $180 ^ { \circ }$ .)

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

At the ball park, Sarah can buy 5 hotdogs and 7 hamburgers for $57 or 7 hotdogs and 3 hamburgers for $39. What is the price of a hotdog?

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). $\left\{ \begin{array} { l } b + 2 c = 10 - a \\a + c = 11 - 2 b \\2 a + b + c = 11\end{array} \right.$