Exam 4: Solving Systems of Linear Equations

Solve. -Chandra has 5 liters of a $56 \%$ solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of $46 \%$ solution?

Solve the system by the substitution method or the addition method. - $\left\{ \begin{array} { l } 3 ( 2 x + y ) = 4 x + 21 \\x - 2 y = 0\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { c } x - y + 2 z = 5 \\5 x + z = 0 \\- x + y - 2 z = - 10\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -The perimeter of a triangle is 29 inches. Three times the length of the longest side minus the length of the shortest side is 25 inches. The sum of the length of the longest side and twice the sum of both the other side lengths is 47 inches. Find the side lengths.

Solve the system. - $\left\{ \begin{array} { r } x - y + 3 z = - 5 \\5 x + z = - 1 \\x + 5 y + z = 9\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } 5 x + 3 y = - 5 \\- 10 x - 6 y = 10\end{array} \right.$

Solve the system. - $\left\{ \begin{aligned}x + y + z & = - 2 \\x - y + 4 z & = 14 \\4 x + 4 y + 4 z & = - 14\end{aligned} \right.$

Solve the problem by writing and using a system of linear equations. -Find the amount of a 11% saline solution a lab assistant should add to 100 cc (cubic centimeters) of a 21% saline solution in order to have a 16% solution.

Solve the system. - $\left\{ \begin{array} { r r } y + 4 z & = 18 \\2 x + y - 2 z & = - 12 \\- 4 x - 2 z & = 4\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 3 \\x + y = 8\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 7 x - 8 y = 8 \\35 x - 40 y = 32\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 23 \\x - y = 15\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations. - (-3,7) 4x=-5-y x+5y=32

Solve. -Find the values of $a , b$ , and $c$ such that the equation $y = a x ^ { 2 } + b x + c$ has ordered pair solutions $( - 2,1 ) , ( - 1,4 )$ , and $( 2 , - 11 )$ .

Solve. -A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 3 hot dogs, 3 bags of potato chips, and 3 soft drinks for $11.25. The price of a hot dog is $0.25 more than the price of a Bag of potato chips. The cost of a soft drink is $1.00 less than the price of two hot dogs. Find the cost Of each item.

Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. -At the local convenience store, 7 bags of chips and 3 containers of dip cost $\$ 33$ . However, 3 bags of chips and 4 containers of dip cost $\$ 25$ . What is the cost of one bag of chips and one container of dip?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 3 x + y = - 5 \\2 x + 3 y = 13\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}y & = 2 x - 4 \\2 y - 8 x & = - 12\end{aligned} \right.$

Solve the system of equations by graphing. - $\left\{\begin{array}{r}x+\frac{3}{4} y=-5 \\x=-2\end{array}\right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } \frac { x } { 7 } + \frac { y } { 14 } = 1 \\\frac { x } { 2 } - \frac { y } { 4 } = 0\end{array} \right.$