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. - $\left\{ \begin{array} { l } 8 x - 3 y = 1 \\8 x - 3 y = 5\end{array} \right.$

Solve the problem. -Khang and Hector live 27 miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is 80% of Khang's. They start out at the same time and meet 3 hours later. Find Hector's rate of speed.

Determine if the given ordered triple is a solution of the system. - (4,-5,3) x+y+z=2 x-y+2z=16 3x+y+z=8

Solve the problem. - $\left\{ \begin{array} { l } - 7 x + 9 y = - 21 \\- 4 x - 2 y = - 12\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } 9 x + 8 y = 12 \\- 4 x - 2 y = - 10\end{array} \right.$

Solve the problem. -Don James wants to invest $69,000 to earn $4210 per year. He can invest in B-rated bonds paying 9% per year or in a Certificate of Deposit (CD) paying 4% per year. How much money should be invested in each to realize Exactly $4210 in interest per year?

Solve the problem. -Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $218. The cost of a child's ticket was $6 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { l } x + 8 y = 0 \\x - 8 y = 32\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - (-4,2,-1) x-y+z=-7 x+y+z=-3 x+y-z=-1

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. - $\left\{\begin{array}{l}x-3 y=-3 \\2 x+3 y=12\end{array}\right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( 2 , - 3,5 ) \\x - y + z = - 6 \\x + y + z = 4 \\x + y - z = 0\end{array} \right.$

Solve the problem. -The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound. They have a 30-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of Raisins so that they hit their target value of $6 per pound for the mixture?

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

Solve the problem. -A newspaper carrier has $12.80 in change. He has two more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?

Solve the problem. -One number is 5 less than a second number. Twice the second number is 5 less than 5 times the first. Find the two numbers.

Solve the problem. -Jimmy is a partner in an Internet-based coffee supplier.The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $6 per pound. Jimmy is creating a medium-price product that will sell for $8 per pound.The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds Of the less expensive regular beans should be added?

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { r } ( - 5,4 , - 3 ) \\x + 4 y + 5 z = - 12 \\3 y + 4 z = - 8 \\z = - 5\end{array} \right.$

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. - $\left\{ \begin{array} { l } x + y = 7 \\x - y = 1\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = - 1 \\x - y = 4\end{array} \right.$

Solve the problem. -If $2000 is invested at 10% annual interest, how much should be invested at 12% annual interest so that the total yearly income from both investments is $5000?