Exam 3: Systems of Equations

An acute angle is an angle with measure less than 90 degrees. In a right triangle, the measure of one acute angle is $24 ^ { \circ }$ greater than two times the measure of the other acute angle. Find the measure of the angles.

Evaluate the determinant. $- 6$ $4 - 3$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 0 \\8 x - 6 y = - 4\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 3 x + y - 3 z = - 5 \\x - 2 y + 4 z = 21 \\x + y + z = 9\end{array} \right.$

If two equations have different graphs, they are called __________ equations. Two equations with the same graph are called __________ equations.

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate. $\sqrt { - 16 } \sqrt { - 64 }$

Solve the system by graphing. $\left\{ \begin{array} { l } x + y = 4 \\x - y = 2\end{array} \right.$

The sum of the measures of the angles of any triangle is 180∘ . In triangle ABC, angle A measures 56∘ less than the sum of the measures of angles B and C, and angle C measures 6∘ less than three times the measure of angle B. Find the measure of angle A.

Consider the system $\left\{ \begin{array} { l } A x + 3 y = - 5 \\3 x - 3 y = 5\end{array} \right.$ . In order for the equations to be dependent, what does the value of A need to be?

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. If the annual income from these investments is $1,060, how much was invested at each rate?

Two airplanes, flying at the same altitude, are tracked using the same coordinate system on a radar screen. One plane is following a path described by the equation $y = \frac { 2 } { 3 } x - 4$ , and the other is following a path described by the equation $2 x = 3 y + 9$ . Is there a possibility of a collision?

Determine the first step in solving the system $\left\{ \begin{array} { l } 6 x + y - 6 z = - 3 \\8 x - 7 y - z = - 12 \\x - 5 y - 4 z = - 3\end{array} \right.$ by matrices.

The jet stream is a wind current that flows across the United States from west to east. Flying with the jet stream, an airplance flew 3,500 miles in 5 hours. Against the same wind, the return trip took 7 hours. Find the speed of the plane in still air and the speed of the jet stream. ________ mph speed of plane in still air ________ mph speed of jet stream

For the following augmented matrix, give the system of equations it represents. $\left[ \begin{array} { c c c | c } 2 & - 2 & 3 & 1 \\3 & 1 & 1 & 0 \\2 & - 4 & 6 & - 7\end{array} \right]$ Equation one =__________ Equation two =__________ Equation three =__________

Use matrices to solve the system of equations. $\left\{ \begin{array} { r } 6 x + y - z = 21 \\x + 2 y + z = 15 \\5 y - z = 23\end{array} \right.$

A $2 \times 3$ matrix has _____ columns.

Use Cramer s Rule to solve the system $\left\{ \begin{array} { l } 2 x - 3 y = 7 \\x - 5 y = 7\end{array} \right.$

Use matrices to solve: $\left\{ \begin{array} { l } 4 a - 2 b + 6 c - 7 d = - 91 \\9 a + 6 b - 7 c - 5 d = - 28 \\8 a - 5 b + 2 c - 4 d = - 4 \\2 a - 4 b - 2 c + 3 d = 77\end{array} \right.$

A metal stamping plant is considering purchasing a new piece of equipment. The machine they currently use has a setup cost of $1,990 and a cost of $6.90 per impression. The new machine has a setup cost of $4,950 and a cost of $4.90 per impression. Find the break point.

Solve the following system of equations by graphing, if possible. Then write the solution as an ordered pair. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 2 y - x = - 4 \\y = \frac { 1 } { 2 } x - 2\end{array} \right.$