Question 1

Solve the system,if possible.? $$\left\{ \begin{array} { l } 
8 x + 5 y + 6 z = 22 \
4 x - 9 y + 2 z = 78 \
7 x - 7 y - 10 z = 57
\end{array} \right.$$ ?

Accepted Answer

A) x = -1,y = 12,z = -2 
B) x = 5,y = -6,z = 2 
C) x = -5,y = 6,z = -2 
D) x = -5,y = 5,z = -2 
E) no solution;inconsistent system 
A) x = -1,y = 12,z = -2 
B) x = 5,y = -6,z = 2 
C) x = -5,y = 6,z = -2 
D) x = -5,y = 5,z = -2 
E) no solution;inconsistent system

Question 2

Solve the system of linear equations.? $$\left\{ \begin{array} { c l } 
x + y + z + w & = - 1 \
- 2 x + y + 3 z - w & = 6 \
2 x + 2 z - 2 w & = - 18 \
2 x + 4 y - 4 z + w & = 5
\end{array} \right.$$

Accepted Answer

A) ? $( - 5,2 , - 1,3 )$ 
B) ? $( - 5,2,3 , - 1 )$ 
C) ? $( 3,2 , - 1 , - 5 )$ 
D) inconsistent 
E) ? $( - 5 , - 1,2,3 )$ 
A) ? $( - 5,2 , - 1,3 )$ 
B) ? $( - 5,2,3 , - 1 )$ 
C) ? $( 3,2 , - 1 , - 5 )$ 
D) inconsistent 
E) ? $( - 5 , - 1,2,3 )$

Question 3

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c } 
4 x - 3 y - 2 z & = & 21 \
6 y - 5 z & = & 5 \
z & = & - 7
\end{array} \right.$$ ?

Accepted Answer

A) ? $( - 2 , - 5 , - 7 )$ 
B) ? $( - 2,5,7 )$ 
C) ? $( - 5,7 , - 2 )$ 
D) ? $( - 2 , - 5,7 )$ 
E) ? $( - 5 , - 7 , - 2 )$ 
A) ? $( - 2 , - 5 , - 7 )$ 
B) ? $( - 2,5,7 )$ 
C) ? $( - 5,7 , - 2 )$ 
D) ? $( - 2 , - 5,7 )$ 
E) ? $( - 5 , - 7 , - 2 )$

Question 4

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​

Accepted Answer

A) $252,000 at 8% $456,000 at 9%
$63,000 at 10% 
B) $252,000 at 9% $456,000 at 8%
$63,000 at 10% 
C) $252,000 at 8% $63,000 at 9%
$63,000 at 9% 
D) $252,000 at 8% $63,000 at 9%
$63,000 at 10% 
E) $252,000 at 8% $63,000 at 9%
$456,000 at 10% 
A) $252,000 at 8% $456,000 at 9%
$63,000 at 10% 
B) $252,000 at 9% $456,000 at 8%
$63,000 at 10% 
C) $252,000 at 8% $63,000 at 9%
$63,000 at 9% 
D) $252,000 at 8% $63,000 at 9%
$63,000 at 10% 
E) $252,000 at 8% $63,000 at 9%
$456,000 at 10%

Question 5

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c } 
x - y + 2 z & = 22 \
3 y - 8 z & = - 9 \
z & = - 9
\end{array} \right.$$ ?

Accepted Answer

A) ? $( - 13 , - 27 , - 9 )$ 
B) ? $( 13 , - 27 , - 9 )$ 
C) ? $( - 13,27 , - 9 )$ 
D) ? $( 13 , - 27,9 )$ 
E) ? $( 13,27 , - 9 )$ 
A) ? $( - 13 , - 27 , - 9 )$ 
B) ? $( 13 , - 27 , - 9 )$ 
C) ? $( - 13,27 , - 9 )$ 
D) ? $( 13 , - 27,9 )$ 
E) ? $( 13,27 , - 9 )$

Question 6

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

Accepted Answer

A) ? $\frac { A } { x ^ { 2 } } + \frac { B } { x + 6 }$ 
B) ? $\frac { A } { x } + \frac { B x } { x + 6 }$ 
C) ? $\frac { A } { x } - \frac { B x } { x + 6 }$ 
D) ? $\frac { A } { x } + \frac { B } { x + 6 }$ 
E) ? $\frac { A } { x ^ { 2 } } + \frac { B x } { x + 6 }$ 
A) ? $\frac { A } { x ^ { 2 } } + \frac { B } { x + 6 }$ 
B) ? $\frac { A } { x } + \frac { B x } { x + 6 }$ 
C) ? $\frac { A } { x } - \frac { B x } { x + 6 }$ 
D) ? $\frac { A } { x } + \frac { B } { x + 6 }$ 
E) ? $\frac { A } { x ^ { 2 } } + \frac { B x } { x + 6 }$

Question 7

Find the value of x,y and z in the figure.​   ​ where a = 3
​

Accepted Answer

A) ​x = 60°,y = 60°,z = 57° 
B) ​x = 60°,y = 63°,z = 57° 
C) ​x = 63°,y = 63°,z = 57° 
D) ​x = 57°,y = 63°,z = 60° 
E) ​x = 60°,y = 60°,z = 60° 
A) ​x = 60°,y = 60°,z = 57° 
B) ​x = 60°,y = 63°,z = 57° 
C) ​x = 63°,y = 63°,z = 57° 
D) ​x = 57°,y = 63°,z = 60° 
E) ​x = 60°,y = 60°,z = 60°

Question 8

Solve the system of linear equations and check any solution algebraically.? $$\left\{\begin{array} { l } 
3 x + 3 y = 0 \
6 x + 3 y - z & = 0 \
12 x + 3 y + 3 z & = 0
\end{array}\right.$$ ?

Accepted Answer

A)  $( - 3,6,12 )$ ? 
B) ?(0,0,0) 
C) ? $( - 3,6 , - 12 )$ 
D) ? $( 3,6,12 )$ 
E) ? $( 3,6 , - 12 )$ 
A)  $( - 3,6,12 )$ ? 
B) ?(0,0,0) 
C) ? $( - 3,6 , - 12 )$ 
D) ? $( 3,6,12 )$ 
E) ? $( 3,6 , - 12 )$

Question 9

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{aligned}
5 x - 3 y + 2 z & = 3 \
2 x + 4 y - z & = 7 \
x - 11 y + 4 z & = 3
\end{aligned} \right.$$ ?

Accepted Answer

A) ? $( - 3,7,3 )$ 
B) No solution 
C) ? $( 3,7 , - 3 )$ 
D) ? $( - 3,7 , - 3 )$ 
E) ? $( 3,7,3 )$ 
A) ? $( - 3,7,3 )$ 
B) No solution 
C) ? $( 3,7 , - 3 )$ 
D) ? $( - 3,7 , - 3 )$ 
E) ? $( 3,7,3 )$

Question 10

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c } 
- 3 x - 9 y - 7 z & = 0 \
4 y + 2 z & = - 8 \
z & = & 6
\end{array} \right.$$

Accepted Answer

A) ? $( 1,6 , - 5 )$ 
B) ? $( - 5,1,6 )$ 
C) ? $( 3 , - 5,6 )$ 
D) ? $( 1 , - 5,6 )$ 
E) ? $( 6 , - 5,1 )$ 
A) ? $( 1,6 , - 5 )$ 
B) ? $( - 5,1,6 )$ 
C) ? $( 3 , - 5,6 )$ 
D) ? $( 1 , - 5,6 )$ 
E) ? $( 6 , - 5,1 )$

Question 11

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 0 , - 3 ) , ( 4,0 )$ ?

Accepted Answer

A) ? $x ^ { 2 } + y ^ { 2 } - 4 x + 3 y = 0$ 
B) ? $x ^ { 2 } - y ^ { 2 } - 4 x - 3 y = 0$ 
C) ? $x ^ { 2 } + y ^ { 2 } - 4 x - 3 y = 0$ 
D) ? $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y = 0$ 
E) ? $x ^ { 2 } - y ^ { 2 } - 4 x + 3 y = 0$ 
A) ? $x ^ { 2 } + y ^ { 2 } - 4 x + 3 y = 0$ 
B) ? $x ^ { 2 } - y ^ { 2 } - 4 x - 3 y = 0$ 
C) ? $x ^ { 2 } + y ^ { 2 } - 4 x - 3 y = 0$ 
D) ? $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y = 0$ 
E) ? $x ^ { 2 } - y ^ { 2 } - 4 x + 3 y = 0$

Question 12

In a particular area of the United States,the electric utility company has determined that the average monthly electric bill (in dollars)for homeowners varies with the average monthly temperature (degrees Fahrenheit)as shown in the table below. $$\begin{array} { | l | l | } 
\hline \begin{array} { l } 
\text { Average monthly temp. } \
{}^\circ\text {F }
\end{array} & \begin{array} { l } 
\text { Average monthly electric bill } \
\$
\end{array} \
\hline 40 & 78 \
\hline 60 & 61 \
\hline 80 & 108 \
\hline
\end{array}$$ Find a least squares regression parabola that models the data and use that to estimate the average monthly electric bill in a month with average temperature of 57 oF.

Accepted Answer

A) y = 0.07(57)2 - 7.85(57)+ 304 = $84 
B) y = 0.06(57)2 - 6.85(57)+ 304 = $108 
C) y = 0.07(57)2 - 5.85(57)+ 304 = $198 
D) y = 0.08(57)2 - 8.85(57)+ 304 = $59 
E) y = 0.08(57)2 - 4.85(57)+ 304 = $287 
A) y = 0.07(57)2 - 7.85(57)+ 304 = $84 
B) y = 0.06(57)2 - 6.85(57)+ 304 = $108 
C) y = 0.07(57)2 - 5.85(57)+ 304 = $198 
D) y = 0.08(57)2 - 8.85(57)+ 304 = $59 
E) y = 0.08(57)2 - 4.85(57)+ 304 = $287

Question 13

Solve the system of linear equations. $$\left\{ \begin{array} { l l } 
- x + 2 y - 5 z & = - 24 \
2 x + 5 z & = 25 \
4 x + 4 y + 3 z & = 21
\end{array} \right.$$

Accepted Answer

A) ? $( - 5,5,2 )$ 
B) ? $( - 2,3,5 )$ 
C) ? $( 5,2 , - 5 )$ 
D) ? $( 5 , - 2,3 )$ 
E) ? $( 5 , - 2,0 )$ 
A) ? $( - 5,5,2 )$ 
B) ? $( - 2,3,5 )$ 
C) ? $( 5,2 , - 5 )$ 
D) ? $( 5 , - 2,3 )$ 
E) ? $( 5 , - 2,0 )$

Question 14

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { c c } 
x + y + z & = 16 \
2 x - y + z & = 18 \
3 x - z & = 19
\end{array} \right.$$ ?

Accepted Answer

A) ? $( 8 , - 3 , - 5 )$ 
B) ? $( - 8 , - 3,5 )$ 
C) ? $( 8,3,5 )$ 
D) ? $( - 8 , - 3 , - 5 )$ 
E) ? $( 8 , - 3,5 )$ 
A) ? $( 8 , - 3 , - 5 )$ 
B) ? $( - 8 , - 3,5 )$ 
C) ? $( 8,3,5 )$ 
D) ? $( - 8 , - 3 , - 5 )$ 
E) ? $( 8 , - 3,5 )$

Question 15

Use back-substitution to solve the system of linear equations. ?? $$\left\{ \begin{array} { c l } 
2 x - y + 5 z & = 24 \
y + 2 z & = 9 \
z & = 7
\end{array} \right.$$ ?

Accepted Answer

A) ? $$( - 8 , - 5,7 )$$ 
B) ?? $$( - 8,5,7 )$$ 
C) ?? $( - 8 , - 5 , - 7 )$ 
D) ?? $( - 7 , - 5,7 )$ 
E) ?? $( - 8 , - 5 , - 5 )$ 
A) ? $$( - 8 , - 5,7 )$$ 
B) ?? $$( - 8,5,7 )$$ 
C) ?? $( - 8 , - 5 , - 7 )$ 
D) ?? $( - 7 , - 5,7 )$ 
E) ?? $( - 8 , - 5 , - 5 )$

Question 16

Determine whether the ordered triple is a solution of the system of equations.? $$\left\{ \begin{array} { l } 
3 x + 4 y - z = 16 \
5 x - y + 2 z = 26 \
2 x - 3 y + 7 z = 30
\end{array} \right.$$ ?? $$( 4,2,4 )$$ ?

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 17

The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​

Accepted Answer

A) 50 ft,33 ft,28 ft 
B) 49 ft,34 ft,28 ft 
C) 49 ft,33 ft,50 ft 
D) 49 ft,33 ft,28 ft 
E) 49 ft,35 ft,28 ft 
A) 50 ft,33 ft,28 ft 
B) 49 ft,34 ft,28 ft 
C) 49 ft,33 ft,50 ft 
D) 49 ft,33 ft,28 ft 
E) 49 ft,35 ft,28 ft

Question 18

Solve the system,if possible. $$\left\{ \begin{array} { l } 
4 x + 3 y + 4 z = - 14 \
3 x - 7 y + 2 z = 46 \
6 x - 9 y - 8 z = 74
\end{array} \right.$$ ​
​

Accepted Answer

The answer of Solve the system,if possible. \[\left\{ \begin{array} {...

Question 19

Solve the system of linear equations.? $$\left\{ \begin{array} { l l } 
- 2 x + 3 y - 4 z & = - 19 \
4 x - y - z & = 22 \
4 x + y - z & = 12
\end{array} \right.$$

Accepted Answer

A) ? $( 1 , - 4 , - 4 )$ 
B) ? $( 4 , - 5 , - 1 )$ 
C) ? $( - 5 , - 1,4 )$ 
D) inconsistent 
E) ? $( - 4,1 , - 4 )$ 
A) ? $( 1 , - 4 , - 4 )$ 
B) ? $( 4 , - 5 , - 1 )$ 
C) ? $( - 5 , - 1,4 )$ 
D) inconsistent 
E) ? $( - 4,1 , - 4 )$

Question 20

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { l l } 
2 x + y - z & = 5 \
x - 2 y + 2 z & = - 7 \
3 x - y + z & = 3
\end{array} \right.$$ ?

Accepted Answer

A) ? $( 5 , - 7,3 )$ 
B) ? $( 5 , - 7 , - 3 )$ 
C) ? $( - 5 , - 7,3 )$ 
D) No solution 
E) ? $( - 5 , - 7 , - 3 )$ 
A) ? $( 5 , - 7,3 )$ 
B) ? $( 5 , - 7 , - 3 )$ 
C) ? $( - 5 , - 7,3 )$ 
D) No solution 
E) ? $( - 5 , - 7 , - 3 )$

Exam 43: Multivariable Linear Systems

Solve the system,if possible.? {8x+5y+6z=224x−9y+2z=787x−7y−10z=57\left\{ \begin{array} { l } 8 x + 5 y + 6 z = 22 \\4 x - 9 y + 2 z = 78 \\7 x - 7 y - 10 z = 57\end{array} \right.⎩⎨⎧​8x+5y+6z=224x−9y+2z=787x−7y−10z=57​ ?

Use back-substitution to solve the system of linear equations.? {4x−3y−2z=216y−5z=5z=−7\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.⎩⎨⎧​4x−3y−2z6y−5zz​===​215−7​ ?

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​

Use back-substitution to solve the system of linear equations.? {x−y+2z=223y−8z=−9z=−9\left\{ \begin{array} { c c } x - y + 2 z & = 22 \\3 y - 8 z & = - 9 \\z & = - 9\end{array} \right.⎩⎨⎧​x−y+2z3y−8zz​=22=−9=−9​ ?

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. 1x2+6x\frac { 1 } { x ^ { 2 } + 6 x }x2+6x1​

Find the value of x,y and z in the figure.​ ​ where a = 3 ​

Solve the system of linear equations and check any solution algebraically.? {3x+3y=06x+3y−z=012x+3y+3z=0\left\{\begin{array} { l } 3 x + 3 y = 0 \\6 x + 3 y - z & = 0 \\12 x + 3 y + 3 z & = 0\end{array}\right.⎩⎨⎧​3x+3y=06x+3y−z12x+3y+3z​=0=0​ ?

Solve the system of linear equations and check any solution algebraically.? {5x−3y+2z=32x+4y−z=7x−11y+4z=3\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.⎩⎨⎧​5x−3y+2z2x+4y−zx−11y+4z​=3=7=3​ ?

Use back-substitution to solve the system of linear equations.? {−3x−9y−7z=04y+2z=−8z=6\left\{ \begin{array} { c c c } - 3 x - 9 y - 7 z & = 0 \\4 y + 2 z & = - 8 \\z & = & 6\end{array} \right.⎩⎨⎧​−3x−9y−7z4y+2zz​=0=−8=​6​

Find the equation of the circle x2+y2+Dx+Ey+F=0x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0x2+y2+Dx+Ey+F=0 that passes through the points. ?? (0,0),(0,−3),(4,0)( 0,0 ) , ( 0 , - 3 ) , ( 4,0 )(0,0),(0,−3),(4,0) ?

Solve the system of linear equations. {−x+2y−5z=−242x+5z=254x+4y+3z=21\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.⎩⎨⎧​−x+2y−5z2x+5z4x+4y+3z​=−24=25=21​

Solve the system of linear equations and check any solution algebraically.? {x+y+z=162x−y+z=183x−z=19\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.⎩⎨⎧​x+y+z2x−y+z3x−z​=16=18=19​ ?

Use back-substitution to solve the system of linear equations. ?? {2x−y+5z=24y+2z=9z=7\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.⎩⎨⎧​2x−y+5zy+2zz​=24=9=7​ ?

The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​

Solve the system,if possible. {4x+3y+4z=−143x−7y+2z=466x−9y−8z=74\left\{ \begin{array} { l } 4 x + 3 y + 4 z = - 14 \\3 x - 7 y + 2 z = 46 \\6 x - 9 y - 8 z = 74\end{array} \right.⎩⎨⎧​4x+3y+4z=−143x−7y+2z=466x−9y−8z=74​ ​ ​

Solve the system of linear equations.? {−2x+3y−4z=−194x−y−z=224x+y−z=12\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.⎩⎨⎧​−2x+3y−4z4x−y−z4x+y−z​=−19=22=12​

Solve the system of linear equations and check any solution algebraically.? {2x+y−z=5x−2y+2z=−73x−y+z=3\left\{ \begin{array} { l l } 2 x + y - z & = 5 \\x - 2 y + 2 z & = - 7 \\3 x - y + z & = 3\end{array} \right.⎩⎨⎧​2x+y−zx−2y+2z3x−y+z​=5=−7=3​ ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Solve the system,if possible.? $\left\{ \begin{array} { l } 8 x + 5 y + 6 z = 22 \\4 x - 9 y + 2 z = 78 \\7 x - 7 y - 10 z = 57\end{array} \right.$ ?

Use back-substitution to solve the system of linear equations.? $\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.$ ?

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Use back-substitution to solve the system of linear equations.? $\left\{ \begin{array} { c c } x - y + 2 z & = 22 \\3 y - 8 z & = - 9 \\z & = - 9\end{array} \right.$ ?

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

Find the value of x,y and z in the figure. where a = 3

Solve the system of linear equations and check any solution algebraically.? $\left\{\begin{array} { l } 3 x + 3 y = 0 \\6 x + 3 y - z & = 0 \\12 x + 3 y + 3 z & = 0\end{array}\right.$ ?

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.$ ?

Use back-substitution to solve the system of linear equations.? $\left\{ \begin{array} { c c c } - 3 x - 9 y - 7 z & = 0 \\4 y + 2 z & = - 8 \\z & = & 6\end{array} \right.$

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 0 , - 3 ) , ( 4,0 )$ ?

Solve the system of linear equations. $\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.$

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.$ ?

Use back-substitution to solve the system of linear equations. ?? $\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.$ ?

The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle.

Solve the system,if possible. $\left\{ \begin{array} { l } 4 x + 3 y + 4 z = - 14 \\3 x - 7 y + 2 z = 46 \\6 x - 9 y - 8 z = 74\end{array} \right.$

Solve the system of linear equations.? $\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.$

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{array} { l l } 2 x + y - z & = 5 \\x - 2 y + 2 z & = - 7 \\3 x - y + z & = 3\end{array} \right.$ ?