System of Linear Equations Chapter Review
Chapter
Chapter 1
Section
System of Linear Equations Chapter Review
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Solutions 25 Videos

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?

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0.00mins
Q1

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.

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1.55mins
Q2

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?

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2.21mins
Q3

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?

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1.40mins
Q4

Solve the linear system graphically.

\displaystyle \begin{array}{lllll} & x + y = 2 \\ & x = 2y + 2 \\ \end{array}

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0.23mins
Q5a

Solve the linear system graphically.

\displaystyle \begin{array}{lllll} & y -x = 1 \\ & 2x - y = 1 \\ \end{array}

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0.19mins
Q5b

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?

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1.34mins
Q6

Use substitution to solve each system.

\displaystyle \begin{array}{lllll} & 2x + 3y = 7 \\ & -2x - 1 = y \\ \end{array}

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1.01mins
Q7a

Use substitution to solve the system.

\displaystyle \begin{array}{lllll} & 3x - 4y = 5 \\ & x -y = 5 \\ \end{array}

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1.00mins
Q7b

Use substitution to solve each system.

\displaystyle \begin{array}{lllll} & 5x + 2y = 18 \\ & 2x + 3y = 16 \\ \end{array}

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1.54mins
Q7c

Use substitution to solve the system.

\displaystyle \begin{array}{lllll} & 9 = 6x - 3y \\ & 4x - 3y = 5 \\ \end{array}

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1.06mins
Q7d

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.

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2.14mins
Q8

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.

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1.23mins
Q9

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}

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2.18mins
Q10

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?

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1.55mins
Q11

Use elimination to solve the linear system.

\displaystyle \begin{array}{lllll} & 2x -3y = 13\\ & 5x - y = 13 \\ \end{array}

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1.13mins
Q12a

Use elimination to solve the linear system.

\displaystyle \begin{array}{lllll} & x - 3y = 0\\ & 3x - 2y = -7 \\ \end{array}

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0.39mins
Q12b

Use elimination to solve the linear system.

\displaystyle \begin{array}{lllll} & 3x + 21 = 5y\\ & 4y + 6 = - 9x\\ \end{array}

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1.31mins
Q12c

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}

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0.58mins
Q12d

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.

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Q13

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.

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2.50mins
Q14

Solve the linear system.

\displaystyle \begin{array}{llll} &2(2x -1) - (y - 4) =11 \\ &3(1 - x) - 2(y - 3) =-7 \\ \end{array}

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Q15

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?

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1.26mins
Q16

Sketch a linear system that has no solution.

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Q17

The linear system 6x + 5y= 10 and ax+ 2y = b has an infinite number of solutions. Determine a and b.

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1.39mins
Q18