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. - \(\left\{ \begin{array} { c } 4 x + y = 12 \\ 16 x + 4 y = 48 \\ \text { \end{array} \right.\)

Determine whether the ordered pair is a solution of the system. - (3,-1) x+y=-4 x-y=-2

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { l } x + y = 6 \\y = 2 x\end{array} \right.$

Solve the problem. -Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $64.85. How many dimes did she deposit?

Solve the problem. -A twin-engined aircraft can fly 1360 miles from city A to city B in 5 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?

Solve the problem. -One number is 2 less than a second number. Twice the second number is 40 more than 5 times the first. Find the two numbers.

Determine if the given ordered triple is a solution of the system. - (-3,3,0) x-y+3z=-12 4x+z=-3 x+4y+z=9

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

Solve the problem. - $\left\{ \begin{array} { c } 3 x + y = 14 \\12 x + 4 y = 56\end{array} \right.$

Solve the problem. -One number is four more than a second number. Two times the first number is 12 more than four times the second number.

Solve the problem. -Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual interest, and the remainder in a mutual fund that paid 11% annual interest. If his total interest for that year was $800, how much Did Kevin invest in the mutual fund?

Solve the problem. -On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $11 each and a number of necklaces at $14 each. She wrote a check for $1590 to pay for the order. How many bracelets And how many necklaces did Rosaria purchase?

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. - $\left\{ \begin{array} { r } x + 4 y = 36 \\8 x + 5 y = 45\end{array} \right.$

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

Solve the problem. - $\left\{ \begin{array} { l } x - 6 = y \\y + 8 = x\end{array} \right.$

Solve the problem. -A loan officer at a bank has $88,000 to lend and is required to obtain an average return of 8% per year. If he can lend at the rate of 9% or the rate of 7%, how much can he lend at the 7% rate and still meet his required return?

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

Solve the problem. -The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $15 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew-peanut mixture that Will sell for $11 per pound. How many pounds of peanuts should be used?