Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 1
Section

MId Chapter Review on Linear Systems

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Solutions
16 Videos

Doreen has $10 to buy apples and pears.

Use each representation below to determine the possible amounts of each type of fruit she can buy.

a) table

b) graph

c) equation

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Q1

Jon downloads music to his MP3 player from a site that charges $12.95 per month and $0.45 per song. Another site charges $8.99 per month and $0.95 per song. Compare the cost of the two sites using a table and a graph.

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Q2

The graph shows how Sally’s weekly earnings vary with the dollar value of the sales she makes at a clothing store.

a) What do the coordinates (1500, 360) mean?

b) Use the graph to determine what Sally earns when her sales are $3200.

c) Use the graph to determine what sales Sally needs to make if she wants to earn $450.

d) Check your answers for parts b) and C) algebraically.

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Q3

a) Determine an equation for the perimeter of any rectangle whose width is 8 cm less than its length.

b) Determine the length of the rectangle whose width is 72 cm.

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Q4

Solve each linear system.

```
\displaystyle
\begin{array}{llllllll}
&y = x+ 4\\
&y = -2x + 1
\end{array}
```

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Q6a

Solve each linear system.

```
\displaystyle
\begin{array}{llllllll}
&y = 4x - 7\\
&2x - 3y =6
\end{array}
```

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Q6b

Solve each linear system.

```
\displaystyle
\begin{array}{llllllll}
& 3x - y =3\\
& 2x + y = 2
\end{array}
```

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Q6c

Solve the linear system.

```
\displaystyle
\begin{array}{llllllll}
& 5x - 2y = 10\\
& 2x + 4y =4
\end{array}
```

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Q6d

Solve the linear system.

```
\displaystyle
\begin{array}{llllllll}
& y = 5x - 8 \\
& 10x - 5y =7
\end{array}
```

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Q7a

Solve the linear system.

```
\displaystyle
\begin{array}{llllllll}
& 2x + y =2\\
& x - \frac{1}{2}y = 4
\end{array}
```

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Q7b

Solve the linear system.

```
\displaystyle
\begin{array}{llllllll}
& x - 4y = -1\\
& -3x + 8y = - 2
\end{array}
```

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Q7c

Solve the linear system.

```
\displaystyle
\begin{array}{llllllll}
& x + y = 0.7\\
& 5x -4y = -1
\end{array}
```

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Q7d

The art department at a school sold 323 tickets to an art show, for a total of$790. Students paid $2 for tickets, and non-students paid $3.50. The principal asked how many non-students attended the art show.

a) Write a system of two linear equations for this situation.

b) Solve the problem by graphing the system.

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Q8

Suppose you are solving the system `y = 2x + m`

and `3x -y = n`

, where `m`

and `$n$ are integers. Could this system have solutions in all four quadrants? Justify your answer.

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Q9

Create a situation that can be represented by a system of linear equations that has the ordered pair (5, 12) as its solution.

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Q10