Textbook

10 Principles of Mathematics Nelson
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 schoolâ€” 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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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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Q18