A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15).Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?y = 5.5x and y = 7.5x + 10y = 7.5x and y = 5.5xy = 7.5x and y = 5.5x + 10y = 7.5x + 10 and y = 5.5x + 10

To determine the correct system of equations representing the costs of the two gyms, let's analyze the information provided in the problem regarding the two lines:

1. First Line (Fit Fast): This gym has a cost that can be modeled by the line that passes through the points (0, 10) and (4, 32):

   • At (0, 10): This suggests that there is a starting cost of $10 when no classes are taken.
   • To find the slope, we use the points (0, 10) and (4, 32): \[ \text{slope} = \frac{32 - 10}{4 - 0} = \frac{22}{4} = 5.5 \]
   • The equation for this line is: \[ y = 5.5x + 10 \]

2. Second Line (Stepping Up): This gym seems to charge a monthly fee plus an additional fee per class, and it passes through (0, 0) and (2, 15):

   • At (0, 0): This suggests there is no base cost when no classes are taken.
   • To find the slope, we use the points (0, 0) and (2, 15): \[ \text{slope} = \frac{15 - 0}{2 - 0} = \frac{15}{2} = 7.5 \]
   • The equation for this line is: \[ y = 7.5x \]

Thus, the system of equations that represents the costs of the two gyms is:

1. \( y = 5.5x + 10 \) (Fit Fast)
2. \( y = 7.5x \) (Stepping Up)

Therefore, the best choice from your options is:

• \( y = 5.5x + 10 \) and \( y = 7.5x \)

you mean y = 7.5x and y = 5.5x + 10?? or y = 7.5x + 10 and y = 5.5x + 10 because they have 10

Apologies for any confusion. Let's clarify the equations representing the two gyms.

1. Fit Fast:

   • It starts with a fixed cost of $10 and charges a fee of $5.5 per class.
   • The equation for Fit Fast is: \[ y = 5.5x + 10 \]

2. Stepping Up:

   • It does not have a fixed cost and charges $7.5 per class.
   • The equation for Stepping Up is: \[ y = 7.5x \]

Thus, the correct system of equations is:

• \( y = 5.5x + 10 \) (for Fit Fast)
• \( y = 7.5x \) (for Stepping Up)

This means that when comparing both gyms based on the equations, we can recognize that Fit Fast includes a base fee of $10, while Stepping Up does not have any base fee when no classes are taken. So, the correct answer is:

• Fit Fast: \( y = 5.5x + 10 \)
• Stepping Up: \( y = 7.5x \)

If you are looking at options, it would be:

• \( y = 5.5x + 10 \) and \( y = 7.5x \)

These equations reflect the costs accurately based on the descriptions you've given for each gym. There are no additional fixed costs for Stepping Up, unlike Fit Fast. Thank you for your understanding!

but that doesnt exist. its one of THESE y = 7.5x and y = 5.5x
y = 7.5x and y = 5.5x + 10
y = 7.5x + 10 and y = 5.5x + 10

Thank you for your clarification. Based on the provided options and the analysis of the equations we derived earlier:

1. Fit Fast: The equation we derived for this gym is: \[ y = 5.5x + 10 \] (This indicates a base cost of $10 plus $5.5 per class.)

2. Stepping Up: The equation we derived for this gym is: \[ y = 7.5x \] (This indicates that there is no base cost, only $7.5 per class.)

Given your options:

1. \( y = 7.5x \) and \( y = 5.5x \) (both describe linear costs without a base, which isn’t accurate for Fit Fast)
2. \( y = 7.5x \) and \( y = 5.5x + 10 \) (this is correct and matches our derived equations)
3. \( y = 7.5x + 10 \) and \( y = 5.5x + 10 \) (this suggests both have a base cost, which is not correct)

Therefore, the correct choice from your options is:

\( y = 7.5x \) and \( y = 5.5x + 10 \)

This reflects that Stepping Up charges $7.5 per class with no base fee, while Fit Fast charges $5.5 per class plus a $10 base fee.

thank you y = 7.5x and y = 5.5x + 10

Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.

y = 7.5x

y = 5.5x + 10

1. Substitute: 7.5x = 5.5x + 10

How many classes could Anna take so that the total cost for the month would be the same?

___ classes

What is the total monthly cost when it is the same for both gyms?

$___

To determine how many classes Anna could take so that the total cost for each gym would be the same, we can solve the equation you provided.

1. Substitute the equations:

From the equations you have:

• \( y = 7.5x \) (for Stepping Up)
• \( y = 5.5x + 10 \) (for Fit Fast)

Set them equal to each other: \[ 7.5x = 5.5x + 10 \]

2. Solve for \( x \):

First, subtract \( 5.5x \) from both sides: \[ 7.5x - 5.5x = 10 \]

This simplifies to: \[ 2x = 10 \]

Now, divide both sides by 2: \[ x = 5 \]

Therefore, Anna could take 5 classes so that the total cost for the month would be the same.

3. Total Monthly Cost:

Now we can find out the total cost when \( x = 5 \). We can use either equation (both will give the same result):

Using the Stepping Up equation: \[ y = 7.5x = 7.5(5) = 37.5 \]

or using the Fit Fast equation: \[ y = 5.5x + 10 = 5.5(5) + 10 = 27.5 + 10 = 37.5 \]

So, the total monthly cost when it is the same for both gyms is $37.50.

Summary:

• Classes: 5 classes
• Total monthly cost: $37.50

because of spams i cant say but heres the answer Complete the statements about the system of linear equations represented by the tables.

The equation representing the left table is

✔ y = 1.5x – 6
.

The equation representing the right table is

✔ y = –4x + 6.1
.

The solution to the system of equations is

✔ (2.2, –2.7)
.

Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8

1. Isolate x in the first equation:

2. Substitute the value for x into the second equation:

3. Solve for y:







4. Substitute y into either original equation:

5. Write the solution as an ordered pair:





x = 7 – 3y

2(7 – 3y) + 4y = 8

14 – 6y + 4y = 8

14 – 2y = 8

–2y = –6

y = 3

x + 3(3) = 7

Let's solve the system of equations step-by-step as outlined in your question:

Given the equations:

1. \( x + 3y = 7 \)
2. \( 2x + 4y = 8 \)

1. Isolate \( x \) in the first equation:

Starting with the first equation: \[ x + 3y = 7 \] Isolating \( x \): \[ x = 7 - 3y \]

2. Substitute the value for \( x \) into the second equation:

Now substitute \( x = 7 - 3y \) into the second equation: \[ 2(7 - 3y) + 4y = 8 \]

3. Solve for \( y \):

Distributing \( 2 \): \[ 14 - 6y + 4y = 8 \]

Combine like terms: \[ 14 - 2y = 8 \] Now, isolate \( y \): \[ -2y = 8 - 14 \] \[ -2y = -6 \] Dividing both sides by \(-2\): \[ y = 3 \]

4. Substitute \( y \) into either original equation:

Now that we have \( y = 3 \), substitute \( y \) back into the first equation to find \( x \): \[ x + 3(3) = 7 \] \[ x + 9 = 7 \] \[ x = 7 - 9 \] \[ x = -2 \]

5. Write the solution as an ordered pair:

The solution to the system of equations is: \[ (x, y) = (-2, 3) \]

Final Answers:

• The solution to the system of equations is (-2, 3).

Which system has no solution?A system of equations. y equals negative 3 x plus 8. 6 x plus 2 y equals negative 4.5.A system of equations. y equals 9 x plus 6.25. negative 18 x plus 2 y equals 12.5.A system of equations. y equals 4.5 x minus 5. negative 3 x plus 2 y equals 6. A system of equations. y equals 3 x plus 9. x plus 8 y equals 12.3

A system of equations has no solution when the lines represented by the equations are parallel. This means they have the same slope but different y-intercepts. Let's analyze each system of equations you provided to determine which one has no solution.

1. System 1:

• \( y = -3x + 8 \)
• \( 6x + 2y = -4.5 \)

To find the slope of the second equation, we can rewrite it in slope-intercept form \( y = mx + b \): \[ 2y = -6x - 4.5 \quad \Rightarrow \quad y = -3x - 2.25 \]

• Slope of line 1: -3
• Slope of line 2: -3
• Different intercepts: Since the intercepts are 8 and -2.25, these lines are parallel. This system has no solution.

2. System 2:

• \( y = 9x + 6.25 \)
• \( -18x + 2y = 12.5 \)

Rearranging the second equation: \[ 2y = 18x + 12.5 \quad \Rightarrow \quad y = 9x + 6.25 \]

• Slope of line 1: 9
• Slope of line 2: 9
• Same intercepts: Since they are the same lines, this system has infinitely many solutions (they are coincident).

3. System 3:

• \( y = 4.5x - 5 \)
• \( -3x + 2y = 6 \)

Rearranging the second equation: \[ 2y = 3x + 6 \quad \Rightarrow \quad y = 1.5x + 3 \]

• Slope of line 1: 4.5
• Slope of line 2: 1.5
• Different slopes: These lines will intersect at one point, so this system has one unique solution.

4. System 4:

• \( y = 3x + 9 \)
• \( x + 8y = 12.3 \)

Rearranging the second equation: \[ 8y = -x + 12.3 \quad \Rightarrow \quad y = -\frac{1}{8}x + \frac{12.3}{8} \]

• Slope of line 1: 3
• Slope of line 2: \(-\frac{1}{8}\)
• Different slopes: These lines will also intersect at one point, so this system has one unique solution.

Conclusion:

The only system of equations that has no solution is System 1:

• \( y = -3x + 8 \)
• \( 6x + 2y = -4.5 \)

These lines are parallel.