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Magazine Problem 7
Solve using the elimination method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. \(x+y=6\) \(-x+3 y=-2\)
Problem 7
Each course at Mt. Regis College is worth either 3 or 4 credits. The members of the men鈥檚 swim team are taking a total of 48 courses that are worth a total of 155 credits. How many 3-credit courses and how many 4-credit courses are being taken?
Problem 8
Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} y &=x-3 \\ 3 x+y &=5 \end{aligned} $$
Problem 8
Solve using the elimination method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. \(\begin{aligned} x+y &=6 \\\\-x+2 y &=15 \end{aligned}\)
Problem 8
Classify each of the following statements as either true or false. The equations \(x+y=5\) and \(2(x+y)=2(5)\) are dependent.
Problem 9
Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} y &=2 x-5 \\ 3 y-x &=5 \end{aligned} $$
Problem 9
Determine whether the ordered pair is a solution of the given system of equations. Remember to use alphabetical order of variables. $$ \begin{aligned} (1,2) ; & 4 x-y=2 \\ 10 x-3 y &=4 \end{aligned} $$
Problem 9
As part of a fundraiser, the Cobble Hill Daycare collected 430 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. If the total value of the cans and bottles was $26.20, how many 5-cent bottles or cans and how many 10-cent bottles or cans were collected?
Problem 9
Solve using the elimination method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. \(4 x-y=1\) \(3 x+y=13\)
Problem 10
Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} y &=2 x+1 \\ x+y &=4 \end{aligned} $$
