Sarah is planning to visit relatives in England and Spain. On the day that she wants to buy the currencies for her trip, one euro costs \$1.50 and one British pound costs \$2.00. Which of the equations represent combinations of these currencies can Sheila buy for \$700?
After a fundraiser, the treasurer for a minor soccer league invested some of the money in a savings account that paid 2.5\%/year and the rest in a government bond that paid 3.5\%/year. After one year, the money earned \$140 in interest. Define two variables, write an equation.
Gary drove his pickup truck from Cornwall to Chatham. He left Cornwall at 8:15 a.m. and drove at a steady 100 km/h along Highway 401. The graph below shows how the fuel in the tank varied over time.
a) What do the coordinates of the point (5, 25.5) tell you about the amount of fuel?
b) How much fuel was in the tank at 11:45 a.m.?
c) The low fuel warning light came on when 6 L of fuel remained. At what time did this light come on?
Ready Car charges \$59/day plus \$0.14/km to rent a car. Best Car charges \$69/day plus \$0.11/km. Set up an equation which you can use to compare these two rental rates. What advice would you give someone who wants to rent a car from one of these companies?
Solve the linear system graphically.
\displaystyle
\begin{array}{lllll}
& x + y = 2 \\
& x = 2y + 2 \\
\end{array}
Solve the linear system graphically.
\displaystyle
\begin{array}{lllll}
& y -x = 1 \\
& 2x - y = 1 \\
\end{array}
Tools-R-Us rents snow blowers for a base fee of \$20 plus \$8/h. Randy's Rentals rents snowblowers for a base fee of \$12 plus \$10/h.
a) Create an equation that represents the cost of renting a snowblower from Tools-R-Us.
b) Create the corresponding equation for Randy?s Rentals.
c) Solve the system of equations graphically.
d) What does the point of intersection mean in this situation?
Use substitution to solve each system.
\displaystyle
\begin{array}{lllll}
& 2x + 3y = 7 \\
& -2x - 1 = y \\
\end{array}
Use substitution to solve the system.
\displaystyle
\begin{array}{lllll}
& 3x - 4y = 5 \\
& x -y = 5 \\
\end{array}
Use substitution to solve each system.
\displaystyle
\begin{array}{lllll}
& 5x + 2y = 18 \\
& 2x + 3y = 16 \\
\end{array}
Use substitution to solve the system.
\displaystyle
\begin{array}{lllll}
& 9 = 6x - 3y \\
& 4x - 3y = 5 \\
\end{array}
Courtney paid a one-time registration fee to join a fitness club. She also pays a monthly fee. After three months, she had paid \$315. After seven months, she had paid \$535. Determine the registration fee and the monthly fee.
A rectangle has a perimeter of 40 m. Its length is 2 m greater than its width.
a) Represent this situation with a linear system.
b) Solve the linear system using substitution.
c) What do the numbers in the solution represent? Explain.
Which linear system below is equivalent to the system that is shown in the graph?
\displaystyle
\begin{array}{llllll}
&\text{A}. &2x - 5y =4 &\text{B}. &x - 3y = -1\\
&&-x + y = 1 && 2x + y = 4 \\
\end{array}
a) Which of the following is an equivalent system of linear equation?
\displaystyle
\begin{array}{lllll}
& -2x -3y = 5\\
& 3x - y = 9 \\
\end{array}
b) What is the solution for above?
Use elimination to solve the linear system.
\displaystyle
\begin{array}{lllll}
& 2x -3y = 13\\
& 5x - y = 13 \\
\end{array}
Use elimination to solve the linear system.
\displaystyle
\begin{array}{lllll}
& x - 3y = 0\\
& 3x - 2y = -7 \\
\end{array}
Use elimination to solve the linear system.
\displaystyle
\begin{array}{lllll}
& 3x + 21 = 5y\\
& 4y + 6 = - 9x\\
\end{array}
Use elimination to solve the linear system.
\displaystyle
\begin{array}{lllll}
& x - \frac{1}{3}y = - 1\\
& \frac{2}{3}x -\frac{1}{4}y = - 1\\
\end{array}
Lily needs 200 g of chocolate that is 86\% cocoa for a cake recipe. He has one kind of chocolate that is 99\% cocoa and another kind that is 70\% cocoa. How much of each kind of chocolate does he need to make the cake? Round your answer to the nearest gram.
A Grade 10 class is raising money for a school— building project in Uganda. To buy 35 desks and 3 chalkboards, the students need to raise $2082. To buy 40 desks and 2 chalkboards, they need to raise $2238. Determine the cost of a desk and the cost of a chalkboard.
Solve the linear system.
\displaystyle
\begin{array}{llll}
&2(2x -1) - (y - 4) =11 \\
&3(1 - x) - 2(y - 3) =-7 \\
\end{array}
Juan is a cashier at a variety store. He has a total of \$580 in bills. He has 76 bills, consisting of \$5 bills and \$10 bills. How many of each type does he have?
Sketch a linear system that has no solution.
The linear system 6x + 5y= 10 and ax+ 2y = b has an infinite number of solutions. Determine a and b.