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Question

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Answer 1

1. Choose the best method to solve by looking at the way the equations are set up for you: Elimination

2. Using the best method, how could you get the x variables to cancel out? Multiply the top equation by -2 and the bottom equation by 3.
3. After you complete step 2, what would your top equation be? -6x - 8y = -96
4. Line them up and add the equations together to get this equation. -6x + 4y = 96
5. Solve for y. y = 12
6. Solve for x. Substitute the value of y in one of the original equations.
3x + 4(12) = 48
3x + 48 = 48
3x = 0
x = 0

Solution: x = 0, y = 12

Answer 2

To solve this system of equations, you can follow these steps:

1. Choose the best method to solve by looking at the way the equations are set up for you:
- The given system of equations can be solved using the Elimination method.

2. Using the Elimination method, you need to get the x variables to cancel out:
- Multiply the top equation by -2.
- Multiply the bottom equation by 2.

3. After completing step 2, your top equation will be:
- -6x - 8y = -96

4. Line up the equations and add them together to eliminate the x variable:
- (-6x - 8y) + (6x + 2y) = (-96) + (60)
- Simplifying the equation, you get:
- -6x + 6x - 8y + 2y = -96 + 60
- The x variables cancel out, leaving you with:
- -6y = -36

5. Solve for y by dividing both sides of the equation by -6:
- -6y = -36
- Divide by -6:
- y = 6

6. Substitute the value of y back into one of the original equations to solve for x:
- Let's use the first equation: 3x + 4y = 48
- Substitute y = 6:
- 3x + 4(6) = 48
- Simplify and solve for x:
- 3x + 24 = 48
- Subtract 24 from both sides:
- 3x = 24
- Divide by 3:
- x = 8

Therefore, the solution to the system of equations is x = 8 and y = 6.

Answer 3

To solve the given system of equations:

1. Determine the best method to solve the system by examining the way the equations are set up. In this case, the system is set up in a way that makes the elimination method a good choice.

2. To cancel out the x variables, you can multiply the top equation by -2. This gives you:

-6x - 8y = -96

Multiply the bottom equation by 2. This gives you:

6x + 2y = 120

3. After completing step 2, the top equation becomes:

-6x - 8y = -96

4. Line up the two equations and add them together. The result is:

-6x - 8y + 6x + 2y = -96 + 120

Simplifying the equation gives:

-6y = 24

5. Solve for y by dividing both sides of the equation by -6:

-6y / -6 = 24 / -6

This simplifies to:

y = -4

6. To solve for x, substitute the value of y (-4) into either of the original equations. Let's use the first equation:

3x + 4(-4) = 48

Simplifying:

3x - 16 = 48

Add 16 to both sides of the equation:

3x = 48 + 16

This gives:

3x = 64

Divide both sides of the equation by 3:

x = 64 / 3

So the value of x is approximately 21.33 (rounded to two decimal places).

Therefore, the solution to the system of equations is x = 21.33 and y = -4.