Exam 43: Multivariable Linear Systems

?Determine which one of the ordered triples below is a solution of the given system of equations. $\left\{ \begin{array} { l l } 5 x + 7 y - 7 z & = 11 \\2 x - 3 y - z & = - 18 \\3 x - 4 y + z & = - 41\end{array} \right.$

Determine whether the ordered triple is a solution of the system of equations.? $\left\{ \begin{aligned}4 x + y - z & = 0 \\- 8 x - 6 y + z & = - \frac { 7 } { 4 } \\3 x - y & = - \frac { 9 } { 4 }\end{aligned} \right.$ ? $\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$ ? ?

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{array} { l } 6 y + 4 z = - 24 \\3 x + 3 y = 21 \\2 x - 3 z = 22\end{array} \right.$ ?

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 0,12 ) , ( 6,6 )$ ?

Solve the system of linear equations.? $\left\{ \begin{array} { c c c } x + y + z & = 2 \\x - y + 2 z & = - 13 \\- 4 y - z & = - 33\end{array} \right.$

The perimeter of a triangle is 170 feet.The longest side of the triangle is 5 feet shorter than twice the shortest side.The sum of the lengths of the two shorter sides is 36 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{array} { c } x + 4 z = 1 \\x + y + 10 z = 10 \\2 x - y + 2 z = - 5\end{array} \right.$ ?

Solve the system of linear equations and check any solution algebraically.? $\left\{ \begin{array} { l } 2 x + 2 z = 14 \\5 x + 3 y = 16 \\3 y - 4 z = 16\end{array} \right.$ ?

A health insurance company advertises on television,on radio,and in the local newspaper.The marketing department has an advertising budget of $45,000 per month.A television ad costs $1,000,a radio ad costs $200 ,and a newspaper ad costs $500 .The department wants to run 70 ads per month,and have as many television ads as radio and newspaper ads combined.How many of each type of ad can the department run each month? ​

Solve the system,if possible. ?? $\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.$ ?

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier. ?? $\left\{ \begin{array} { l } 2 + 2 y + 2 \lambda = 0 \\2 x + 1 + \lambda = 0 \\2 x + y - 96 = 0\end{array} \right.$ ?

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. ?? $( 0,0 ) , ( 4 , - 4 ) , ( 8,0 )$ ?

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier.? $\left\{\begin{array}{ll}2 x+\lambda & =0 \\2 y+\lambda & =0 \\x+y-10 & =0\end{array}\right.$ ?

Perform the row operation and find the equivalent system. Add Equation 1 to Equation 2.? $\left\{ \begin{array} { c c c } x - 4 y + 5 z & = 9 & \text { Equation 1 } \\- x + 5 y - 9 z & = 8 & \text { Equation 2 } \\4 x - 5 z & = 0 & \text { Equation 3 }\end{array} \right.$ ?

Determine whether the statement is true or false. ​ If a system of three linear equations is inconsistent,then its graph has one points common to all three equations. ​

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )$ .

A chemist needs 10 liters of a 25% acid solution.The solution is to be mixed from three solutions whose concentrations are 10%,20%,and 50%.How many liters of each solution will satisfy each condition? Use 2 liters of the 50% solution. ​

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. $( - 1,4 ) , ( 0,4 ) , ( 1,0 )$ ?

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 6,6 ) , ( 12,0 )$ ?

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier.? $\left\{ \begin{array} { c } 5 x - 5 x \lambda = 0 \\- 2 y + \lambda = 0 \\y - x ^ { 2 } = 0\end{array} \right.$ ?