Exam 4: Systems of Linear Equations

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } \frac { x + 5 } { 3 } = \frac { y + 19 } { 6 } \\\frac { x } { 2 } = \frac { 2 y + 8 } { 4 }\end{array} \right.$

Solve the problem. -A chemist needs 12 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 9 x + 5 y = 51 \\7 x - 2 y = 75\end{array} \right.$

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 2 x + 10 y = - 64 \\9 x + 2 y = 56\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } y = 5 x + 4 \\y = 8 x + 3\end{array} \right.$

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } x + y = 8 \\x + y = 4\end{array} \right.$

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 2 x - 5 y = 5 \\3 x - 4 y = 5\end{array} \right.$

Solve the problem. -The radiator in a certain make of car needs to contain 40 liters of 40% antifreeze. The radiator now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze To get the desired strength?

Solve the problem. - $\left\{ \begin{array} { l } x + y = - 9 \\x - y = 19\end{array} \right.$

Solve the problem. -A bank loaned out $57,000, part of it at the rate of 11% per year and the rest at a rate of 7% per year. If the interest received was $4990, how much was loaned at 11%?

Solve the problem. - $\left\{ \begin{array} { l } - 2 x - 6 y = - 3 \\4 x + 12 y = 0\end{array} \right.$

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{\begin{array}{l}4 x+y=12 \\16 x+4 y=48\end{array}\right.$

Solve the problem. -Two numbers total 12, and their difference is 16. Find the two numbers.

Solve the problem. - $\left\{ \begin{array} { r } x + 2 y = 2 \\9 x + 3 y = 3\end{array} \right.$

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $34.72. The second group bought 5 slices of pizza and 5 soft drinks for $ 26)50. How much does one slice of pizza cost?

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { r } ( - 3,2 , - 2 ) \\x + 5 y + 3 z = 1 \\2 y + 4 z = - 4 \\z = - 2\end{array} \right.$

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 8 x + 98 = 6 y \\- 3 x - 4 y = - 7\end{array} \right.$

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{\begin{array}{l}y=x+6 \\y=-3 x-2\end{array}\right.$

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 7 x - 2 y = 6 \\- 21 x + 6 y = - 24\end{array} \right.$

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - $\left\{ \begin{array} { c } x + 4 y = - 17 \\2 x + 4 y = - 18\end{array} \right.$