Exam 4: Systems of Linear Equations

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. - $\left\{ \begin{array} { l } 2 x - y = - 8 \\y = 2\end{array} \right.$

Solve the problem. -How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get an 80% acid solution?

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. - $\left\{ \begin{array} { l } \frac { 1 } { 2 } x - y = 1 \\x = 2\end{array} \right.$

Solve the problem. -A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much Should they invest in each to realize exactly $15,600 per year?

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. - $\left\{ \begin{array} { l } 3 x + \frac { 1 } { 4 } y = - 7 \\5 x + \frac { 1 } { 3 } y = - \frac { 34 } { 3 }\end{array} \right.$

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. - $\left\{ \begin{array} { r } x + 7 y = 68 \\3 x + 7 y = 78\end{array} \right.$

Solve the problem. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $5.25. Another customer buys 4 hot dogs and 4 bags of potato chips for $9.00. Find the cost of each item.

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. - $\left\{ \begin{array} { l } 6 x - 12 = 6 y \\2 x + 2 y = - 20\end{array} \right.$

Determine whether the ordered pair is a solution of the system. -(4, -2) $\left\{ \begin{array} { l } 2 x = 6 - y \\3 x = 8 - 2 y\end{array} \right.$

Solve the problem. -Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 3 times the width. He needs 50 feet of fencing to do the job. Find the length and Width of the garden.

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { c } x + 8 y = - 61 \\8 x + 7 y = - 89\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } y = 2 x + 4 \\4 x + y = - 8\end{array} \right.$

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

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. - $\left\{\begin{array}{l}x=8 \\x=-5\end{array}\right.$

Solve the system by the best method. Use set notation to express the solution set. - \(\left\{ \begin{array} { r } 4 x = - 4 - 8 y \\ 2 x - 5 y = 34 \\ \text { \end{array} \right.\)

Solve the problem. -Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 3 hours on the road. Doreen can maintain a speed of 2.4 miles per hour, which is 40% of Irena's Speed. If they meet exactly as planned, what is the distance between their houses?

Solve the problem. -The sum of two numbers is -5. Three times the first number equals 2 times the second number. Find the two numbers.

Solve the problem. -Keema cashed her paycheck and came home from the bank with $820 in bills of the following denominations: twenties, fives, and hundreds. She has eight times as many fives as twenties and five more hundreds as Twenties. How many of each denomination does she have?

Solve the problem. -The three angles in a triangle always add up to 180°. If one angle in a triangle is 56° and the second is 3 times the third, what are the three angles?

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. - $\left\{\begin{array}{l}3 x+y=-7 \\2 x+y=-6\end{array}\right.$