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Solutions
45 Videos

Write the linear system that corresponds to each equation.

`4x - 5 = 3`

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0.34mins

Q1a

Write the linear system that corresponds to each equation.

`\frac{1}{2}x + 3 = 5`

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0.38mins

Q1b

Write the linear system that corresponds to each equation.

`-2(x -3) = -4`

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0.44mins

Q1c

Write the linear system that corresponds to each equation.

`\frac{1}{4}(x + \frac{2}{5}) = 0`

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1.00mins

Q1d

Solve each equation using algebra.

`3x + 6 =12`

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0.11mins

Q2a

Solve each equation using algebra.

`5 - 2x = 11`

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0.12mins

Q2b

Solve each equation using algebra.

`4x - 8 = 12`

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0.11mins

Q2c

Solve each equation using algebra.

`-6x + 8 = -10`

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0.13mins

Q2d

Determine the x-intercept of each of the following.

`y = -5x +20`

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0.16mins

Q3a

Determine the x-intercept of each of the following.

`2x + y = 10`

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0.12mins

Q3b

A promoter is holding a video dance. Tickets cost `\$15`

per person, and he has given away 10 free tickets to radio stations.

- Create the linear relation that models the money the promoter will earn in ticket sales in terms of the number of people attending the dance.

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1.02mins

Q4a

A promoter is holding a video dance. Tickets cost `\$15`

per person, and he has given away 10 free tickets to radio stations.

Here is the linear equation that represents the above.
```
\displaystyle
R = 15n - 150
```

- Graph the linear relation.

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0.24mins

Q4b

A promoter is holding a video dance. Tickets cost `\$15`

per person, and he has given away 10 free tickets to radio stations.

Here is the linear equation that represents the above.
```
\displaystyle
R = 15n - 150
```

and below is the graph

- Write the equation you would use to determine how many people attended if ticket sales were only \$600. Estimate the solution using the graph.

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0.32mins

Q4c

`\$15`

per person, and he has given away 10 free tickets to radio stations.

Find how many people bought the ticket if he made `\$600`

?

You may use the equation below.

```
\displaystyle
R = 15n - 150
```

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0.25mins

Q4d

Erin joins a CD club. The first 10 CDs are free, but after that she pays `\$15.95`

for each CD she orders.

- Write an expression for the cost of
`x`

CDs.

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0.46mins

Q6a

Erin joins a CD club. The first 10 CDs are free, but after that she pays `\$15.95`

for each CD she orders.

- How much would she pay for 15 CDs?

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0.15mins

Q6b

Erin joins a CD club. The first 10 CDs are free, but after that she pays `\$15.95`

for each CD she orders.

It can be modelled by ```
\displaystyle
Cost = 15.95x - 159.5
```

- Erin receives her first order of CDs with a bill for
`\$31.90`

. Create and solve an equation to determine how many she ordered.

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0.37mins

Q6c

Solve the equation.

`9x + 2 = 11x -10`

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0.19mins

Q7a

Solve the equation.

`-\frac{4}{5}x + \frac{2}{3}= 1\frac{3}{4}x +2`

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1.24mins

Q7b

Solve the equation.

`-3(x + 1) -2 = 4x - 5(x - 3)`

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0.41mins

Q7c

Solve the equation.

`\dfrac{(4+x)}{3} +4 = \dfrac{x - 6}{2} - 6`

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1.10mins

Q7d

Determine the length of each base for the trapezoids below if they have the same area.

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0.57mins

Q8

Is `x = 3`

the solution to `5(3x - 2) =4 -10(x + 1)`

? Explain how you know.

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0.32mins

Q9

Solve each equation for the variable indicated.

`P = 2l + 2w; l`

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0.27mins

Q10a

Solve each equation for the variable indicated.

`A = P + Prt; t`

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0.31mins

Q10b

Solve each equation for the variable indicated.

`V =\pi r^2h; h`

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0.35mins

Q10c

Solve each equation for the variable indicated.

`A x + By = C; y`

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0.45mins

Q10d

For formula `C =\frac{5}{9}(F- 32)`

is used to convert Fahrenheit temperatures to Celsius.

Determine the Celsius temperature when `F = 90`

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0.24mins

Q11a

For formula `C =\frac{5}{9}(F- 32)`

is used to convert Fahrenheit temperatures to Celsius.

Solve for `F`

in terms of `C`

.

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0.31mins

Q11b

For formula `C =\frac{5}{9}(F- 32)`

is used to convert Fahrenheit temperatures to Celsius.

Determine the Fahrenheit temperature when `C = 25`

.

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0.22mins

Q11c

Solve for `y`

in terms of `x`

.

`8x - 4y =12`

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0.27mins

Q12a

Solve for `y`

in terms of `x`

.

`5x = 10y - 20`

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0.31mins

Q12b

Solve for `y`

in terms of `x`

.

`3x - 3y -9 = 0`

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0.31mins

Q12c

Solve for `y`

in terms of `x`

.

`\frac{x}{4} + \frac{y}{2} =2`

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0.29mins

Q12d

Jose has `\$32.00`

in loonies and toonies.

- Write a linear relation expressing the total amount of money in terms of the number of loonies and toonies..

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0.52mins

Q13a

Jose has `\$32.00`

in loonies and toonies.

- Write an equation to express the number of toonies in terms of the number of loonies.

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0.19mins

Q13b

Jose has `\$32.00`

in loonies and toonies.

- Use your equation to determine which one of the following is a possible combination of coins Josh could have.

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1.03mins

Q13c

Jose has `\$32.00`

in loonies and toonies.

- Is it possible that Jose has 13 toonies and 5 loonies? Explain.

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0.25mins

Q13d

Solve the equation `4 = -2x -3`

byI graphing `y = -2x -3`

and `y =4`

. The x-value where the two lines intersect is the solutions.

a) What is the solution to this equation based on the graph?

b) Verify the solution using algebra.

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0.47mins

Q14ab

Solve the equation `4 = -2x -3`

byI graphing `y = -2x -3`

and `y =4`

. The x-value where the two lines intersect is the solutions.

How could you use this strategy to solve `3x -4 = 2x + 3`

?

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1.01mins

Q14d

Solve each of the following systems of equations using a graph.

`3x - 4y = -12`

and`2x - 3y = 64`

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0.59mins

Q15c

Fitness centre A has a monthly membership fee of `\$90`

. Members pay $5 to take an aerobics class. At Fitness centre B, there is no membership fee, but clients pay `\$10`

per class.

a) Write a linear relation for the yearly cost in terms of the number of aerobics classes.

b) Graph the equations on the same set of axes.

c) State the point of intersection.

d) What does the point of intersection mean in this case?

e) How would you advise someone who is trying to choose between the two fitness clubs?

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0.00mins

Q16

The Video Stream you can watch movies for `\$ 3.00/month`

each and has no membership fee. At Rent Stream you can view movies for `\$2/month`

but has a `\$15`

membership fee.

a) Write an equation for each situation.

b) Graph both equations on the same set of axes. Find the point of intersection.

c) What does the point of intersection mean in this case?

d) What advice would you give to someone who is deciding which video store to use?

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Q17