Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. ? 00 The system has no solution. The system has a unique solution: 5x-y=-9 (x,y)=(.) -5x+y=9 The system has infinitely many solutions. System B 5x-6y=1 -5x+6y=2 The system has no solution. The system has a unique solution: (x,y)=(. The system has infinitely many solutions.

Answer 1

Let's analyze each system of equations individually.

System A:

1. \( 5x - y = -9 \)
2. \( -5x + y = 9 \)

To solve this system, we can rearrange the second equation:

From the second equation: \[ -5x + y = 9 \implies y = 5x + 9 \]

Now substitute \( y \) into the first equation:

\[ 5x - (5x + 9) = -9 \] \[ 5x - 5x - 9 = -9 \] \[ -9 = -9 \]

This is a true statement, which indicates that the two equations are dependent (they are essentially the same line represented in different forms). Thus, the system has infinitely many solutions.

Solution for System A:

The solution can be expressed in terms of \( x \): \[ y = 5x + 9 \] Where \( x \) can be any real number.

Summary for System A:

• The system has infinitely many solutions.

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System B:

1. \( 5x - 6y = 1 \)
2. \( -5x + 6y = 2 \)

To solve this system, we can rearrange the second equation:

From the second equation: \[ -5x + 6y = 2 \implies 6y = 5x + 2 \implies y = \frac{5}{6}x + \frac{1}{3} \]

Now substitute \( y \) into the first equation:

\[ 5x - 6\left(\frac{5}{6}x + \frac{1}{3}\right) = 1 \] \[ 5x - 5x - 2 = 1 \] \[ -2 = 1 \]

This is a false statement, indicating that the two equations represent parallel lines that do not intersect. Thus, the system has no solution.

Summary for System B:

• The system has no solution.

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Final Answer:

• System A: The system has infinitely many solutions.
• System B: The system has no solution.

Answer 2

i need the x and y equation for both systems

Answer 3

Sure! Let's express both systems in terms of \( y \) as a function of \( x \), and also find specific points for both systems of equations.

System A:

1. \( 5x - y = -9 \)
2. \( -5x + y = 9 \)

We already rearranged the first equation. Let’s do it more explicitly:

From the first equation: \[ 5x - y = -9 \] Rearranging gives: \[ y = 5x + 9 \quad (1) \]

For the second equation: \[ -5x + y = 9 \] Rearranging gives: \[ y = 5x + 9 \quad (2) \]

Both equations are equivalent. Therefore, the relationship between \( x \) and \( y \) is:

System A:

• \( y = 5x + 9 \)

This means there are infinitely many solutions of the form \( (x, 5x + 9) \) for any \( x \).

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System B:

1. \( 5x - 6y = 1 \)
2. \( -5x + 6y = 2 \)

For the first equation: \[ 5x - 6y = 1 \] Rearranging gives: \[ -6y = 1 - 5x \] \[ y = \frac{5}{6}x - \frac{1}{6} \quad (1) \]

For the second equation: \[ -5x + 6y = 2 \] Rearranging gives: \[ 6y = 5x + 2 \] \[ y = \frac{5}{6}x + \frac{1}{3} \quad (2) \]

However, since the conditions resulted in a contradiction, we can conclude that the lines represented by equations in System B are parallel.

System B:

Overall, since System B does not have any solutions, we cannot provide valid \( (x, y) \) pairs. The lines do not intersect.

Summary:

• System A: \( y = 5x + 9 \) (infinitely many solutions)
• System B: No solutions, (parallel lines).

If you have any further questions or need specific values (such as intersecting points or a specific range), feel free to ask!

Answer 4

its only two numbers like this: _6_ , _7_

Answer 5

Got it! Let's find the specific coordinates in the format you're looking for.

For System A

We have the equation: \[ y = 5x + 9 \]

To provide a specific solution, we can choose a value for \( x \). Let's choose \( x = 0 \): \[ y = 5(0) + 9 = 9 \] So one solution is: \[ (0, 9) \rightarrow (x, y) = (0, 9) ; \text{or you can just take the constants as } 0, 9 \]

For System B

This system has no solution, as the equations represent parallel lines.

Thus, since there are no intersection points, we cannot provide \( x \) and \( y \) numbers for System B.

Summary of the values:

• System A: \( \underline{0}, \underline{9} \)
• System B: No solution (cannot provide numbers).

If you need any other specific numbers for System A or if you want to explore different \( x \) values, let me know!

Answer 6

BOTH OF THOSE ARE INCORECT TRY AND DO IT AGAIN CORRECTLY I DONT WANT TO FAIL

Answer 7

I apologize for any confusion. Let’s solve both systems again carefully and provide the required values in the format you specified.

System A

1. \( 5x - y = -9 \)
2. \( -5x + y = 9 \)

Let's solve the first equation for \( y \):

\[ 5x - y = -9 \implies y = 5x + 9 \]

Now, substituting for \( y \) in the second equation to confirm their equivalence:

\[ -5x + (5x + 9) = 9 \]

This simplifies to:

\[ -5x + 5x + 9 = 9 \implies 9 = 9 \]

Since this is always true, both equations represent the same line. Therefore, there are infinitely many solutions.

Specific Solution for System A

Let’s choose a specific value for \( x \) to find a corresponding \( y \). Let \( x = 0 \): \[ y = 5(0) + 9 = 9 \] So one specific solution is: \[ (x, y) = (0, 9) \]

For System B

1. \( 5x - 6y = 1 \)
2. \( -5x + 6y = 2 \)

Let’s analyze the two equations by solving them:

Starting with the first equation for \( y \): \[ 5x - 6y = 1 \implies -6y = 1 - 5x \implies y = \frac{5}{6}x - \frac{1}{6} \]

Now rearranging the second equation: \[ -5x + 6y = 2 \implies 6y = 5x + 2 \implies y = \frac{5}{6}x + \frac{1}{3} \]

To find if there are solutions, we set the two expressions for \( y \) equal to each other:

\[ \frac{5}{6}x - \frac{1}{6} = \frac{5}{6}x + \frac{1}{3} \]

Subtracting \( \frac{5}{6}x \) from both sides gives: \[ -\frac{1}{6} = \frac{1}{3} \] This is inconsistent, meaning the lines are parallel and there is no solution.

Summary

• System A: A specific solution is \( \underline{0}, \underline{9} \).
• System B: No solution (so no values).

If you have specific points or formats needed, please let me know, and I’ll be glad to assist further!

Answer 8

how many times must i say that is the WRONG answer

Answer 9

I apologize for the confusion and any frustration caused. Let's solve the systems step-by-step and clarify the correct answers.

System A:

1. \( 5x - y = -9 \)
2. \( -5x + y = 9 \)

Step 1: Solve both equations.

From the first equation: \[ 5x - y = -9 \implies y = 5x + 9 \]

From the second equation: \[ -5x + y = 9 \implies y = 5x + 9 \]

Both equations represent the same line, meaning there are infinitely many solutions.

We can set \( x = 0 \) to find a specific point: \[ y = 5(0) + 9 = 9 \]

Therefore, a specific solution could be:

• (0, 9)

Now for System B:

1. \( 5x - 6y = 1 \)
2. \( -5x + 6y = 2 \)

Step 1: Solve both equations.

From the first equation: \[ 5x - 6y = 1 \implies 6y = 5x - 1 \implies y = \frac{5}{6}x - \frac{1}{6} \]

From the second equation: \[ -5x + 6y = 2 \implies 6y = 5x + 2 \implies y = \frac{5}{6}x + \frac{1}{3} \]

Step 2: Set the equations equal to each other to see if they intersect.

To check for consistency: \[ \frac{5}{6}x - \frac{1}{6} = \frac{5}{6}x + \frac{1}{3} \]

Subtracting \(\frac{5}{6}x\) from both sides: \[ -\frac{1}{6} = \frac{1}{3} \]

This is a contradiction (since \(-\frac{1}{6} \neq \frac{1}{3}\)). Therefore, there are no solutions for System B.

Summary:

• System A: \(\underline{0}, \underline{9}\) (indicating infinite solutions, but we provide one specific pair)
• System B: No solution (indicating no points can be given).

If you need specific points other than (0, 9) for System A or want me to summarize anything differently, please clarify, and I’ll provide the exact information you require. Thank you for your patience!

Answer 10

you are helpless

Answer 11

I apologize for the confusion and frustration. Let's go through it one more time carefully to ensure we get the right answers.

System A:

1. \( 5x - y = -9 \)
2. \( -5x + y = 9 \)

We can solve this system step by step.

Step 1: Solve System A

Let's start with the first equation: \[ 5x - y = -9 \implies y = 5x + 9 \]

Now, substitute \( y \) from the first equation into the second equation: \[ -5x + (5x + 9) = 9 \]

This simplifies to: \[ 9 = 9 \]

This tells us that the two lines are identical, and thus, there are infinitely many solutions. However, we can express the relationship or provide a specific example.

A specific solution:

Let's choose \( x = 0 \): \[ y = 5(0) + 9 = 9 \] So, one specific solution is: \[ \text{Solution A: } (0, 9) \]

System B:

1. \( 5x - 6y = 1 \)
2. \( -5x + 6y = 2 \)

Step 2: Solve System B

From the first equation: \[ 5x - 6y = 1 \implies 6y = 5x - 1 \implies y = \frac{5}{6}x - \frac{1}{6} \]

From the second equation: \[ -5x + 6y = 2 \implies 6y = 5x + 2 \implies y = \frac{5}{6}x + \frac{1}{3} \]

Step 3: Set the two \( y \) equations equal to each other:

\[ \frac{5}{6}x - \frac{1}{6} = \frac{5}{6}x + \frac{1}{3} \] Subtract \( \frac{5}{6}x \) from both sides: \[ -\frac{1}{6} = \frac{1}{3} \] This is a contradiction.

Conclusion:

System B has no solution.

In conclusion:

• For System A: A specific solution is \( \underline{0}, \underline{9} \).
• For System B: There are no solutions. (No values to provide).

If you need further help or specific formats for how the answers are given, please let me know, and I will do my best to assist you accurately. Thank you for your patience, and I’m here to help.