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2 years ago

Solving systems of equations algebraically.

Mathematics

1 answer:

Elanso [62]2 years ago

8 0

Answer:

x = 2

y = -1

Step-by-step explanation:

Since it gives you the value of y already, just plug that into the equation, like so:

y = 4x - 9

x - 3 = 4x - 9

Subtract the x from both sides:

x - 3 = 4x - 9

-x - x

__________

-3 = 3x - 9

Then, add 9 to both sides:

-3 = 3x - 9

+9 + 9

________

6 = 3x

Divide both sides by 3:

2 = x

Now plug in x for y:

y = x - 3

y = 2 - 3

y = -1

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Elena is paid a constant rate for each hour she works. The table shows the amounts of money that Elena earned for various amount

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Constant rates are used to illustrate linear functions.

The average rate of change is $9.0 per hour
The function that models the table is: $\mathbf{f(x) = 9x }$
The amount earned in 7.5 hours is $67.5

(a) The average rate of change

This is calculated using:

$\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}$

So, we have:

$\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}$

$\mathbf{Rate = \frac{9}{1.0}}$

$\mathbf{Rate = 9.0}$

Hence, the average rate of change is $9.0 per hour

(b) A function that models the table of values

Let x represent hours, and y represent the earnings.

So, we have:

$\mathbf{y =m (x - x_1) + y_1}$

Where:

m =Rate = 9.0

So, we have:

$\mathbf{y = 9(x - 2.5) + 22.5}$

Expand

$\mathbf{y = 9x - 22.5 + 22.5}$

$\mathbf{y = 9x }$

Represent as a function

$\mathbf{f(x) = 9x }$

Hence, the function that models the table is: $\mathbf{f(x) = 9x }$

(c) Amount earned for 7.5 hours

This means that x = 7.5

So, we have:

$\mathbf{f(7.5) = 9 \times 7.5 }$

$\mathbf{f(7.5) = 67.5}$

Hence, the amount earned in 7.5 hours is $67.5