Exam 3: Systems of Equations

Determine whether the given ordered triple is a solution of given system. $( - 3,2 , - 1 ) , \left\{ \begin{array} { l } 2 x + 2 y + 3 z = - 1 \\3 x + y - z = - 6 \\x + y + 2 z = 1\end{array} \right.$

$\left| \begin{array} { c c c } x & y & 1 \\A & - 1 & 1 \\3 & 2 & 1\end{array} \right| = 0$ represents the equation of a line. Find the value of A so that the line passes through the point (10,5).

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 2 x + y - 3 z = - 17 \\3 x - y + 2 z = - 2 \\- 2 x - y - z = 1\end{array} \right.$

Find the z -coordinate of the solution of the system $\left\{ \begin{array} { l } x - y + z = 5 \\x + 2 y - z = - 3 \\x + y - 5 z = - 5\end{array} \right.$ .

Solve the system using the substitution method, if possible. $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$

A news van and a helicopter left a TV station parking lot at the same time, but headed in opposite directions. They were covering breaking news stories that were 97 miles apart. If the helicopter had to travel 55 miles farther than the van, how far did the van have to travel to reach the location of the news story?

Solve the system by elimination if possible. $\log _ { 6 } x + \log _ { 6 } ( x - 20 ) = \log _ { 6 } 189$

In solving a system of equations by the elimination method, the result 7 = 7 is obtained. Which of the following statements is true?

Use Cramer s Rule to solve for x in the following system. $\left\{ \begin{array} { l } 2 x - 6 y = - 8 \\2 x + 2 y = 7\end{array} \right.$

For the system $\left\{ \begin{array} { l } 3 x + 2 y = 1 \\7 x - y = 3\end{array} \right.$ , $D _ { x } = - 7$ , $D _ { y } = 2$ and $D = - 17$ . What is the solution of the system?

For the system $\left\{ \begin{array} { l } 3 x + y + z = 0 \\x - 2 y + 5 z = 14 \\x + y - 5 z = - 12\end{array} \right.$ , $D _ { x } = 0$ , $D _ { y } = - 56$ , and $D = 28$ . What is the solution of the system?

Write the system of equations represented by the augmented matrix. $\left[ \begin{array} { c c | c } 1 & - 1 & - 5 \\0 & 1 & 4\end{array} \right]$ __________ Use back substitution to find the solution. __________

Find the value of c in the quadratic equation, $y = a x ^ { 2 } + b x + c$ , if the parabola passes through the points (4, 4), (1, 8), and ( 3, 4).

Solve the system by any method, if possible. $\log _ { 7 } \frac { x y } { 7 }$

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

Determine whether the given ordered triple is a solution of given system. $( 5,1,1 ) , \left\{ \begin{array} { l } x - y + z = 5 \\2 x + y - z = 10 \\2 x - 3 y + z = 8\end{array} \right.$

Find the y -coordinate of the solution of the following system. Use the method of substitution. $- \sqrt { - 36 }$

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 $y = \frac { 2 } { 5 } x - 2$ , and the other is following a path described by the equation $5 x = 2 y + 7$ . Is there a possibility of a collision?

An acute angle is an angle with measure less than 90 degrees. In a right triangle, the measure of one acute angle is 39∘ greater than two times the measure of the other acute angle. Find the measure of each acute angle. __________ $\text { o (smaller) }$ __________ $\text { ° (larger) }$

Tell whether the ordered pair (4,-5) is a solution of the system of equations. $\left\{ \begin{array} { l } y + 4 = \frac { 1 } { 4 } x \\5 x + 4 y = 0\end{array} \right.$