Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11 (10 points)

Question

question choices. y=-4,-7(2y+11)-2y=-13,-14y-77-2y=-13,x=3,x+8=11,(3,-4),-16=64,x-2(-4)=11,x-2y=11-->x=2y+11,-16y-77=-13

Answer 1

To solve the system of equations by substitution, we will go through the steps systematically. Let's begin by organizing the equations:

1. \( -7x - 2y = -13 \) (Equation 1)
2. \( x - 2y = 11 \) (Equation 2)

Now let's break down the process:

1. Start with Equation 2: \( x - 2y = 11 \).
2. Solve for \( x \): \( x = 2y + 11 \).
3. Substitute this expression for \( x \) into Equation 1: \[ -7(2y + 11) - 2y = -13 \].
4. Distribute: \[ -14y - 77 - 2y = -13 \].
5. Combine like terms: \[ -16y - 77 = -13 \].
6. Add 77 to both sides: \[ -16y = 64 \].
7. Divide by -16: \[ y = -4 \].
8. Substitute \( y = -4 \) back into Equation 2 to find \( x \): \[ x - 2(-4) = 11 \rightarrow x + 8 = 11 \rightarrow x = 3 \].
9. The solution to the system is \( (3, -4) \).

Now, let's put these steps in order according to your provided choices:

1. \( x - 2y = 11 \rightarrow x = 2y + 11 \).
2. \( -7(2y + 11) - 2y = -13 \).
3. \( -14y - 77 - 2y = -13 \).
4. \( -16y - 77 = -13 \).
5. \( -16 = 64 \).
6. \( y = -4 \).
7. \( x + 8 = 11 \).
8. \( x = 3 \).
9. \( (3, -4) \).

With this in mind, the ordered steps to solve the system using substitution are:

1. \( x - 2y = 11 \rightarrow x = 2y + 11 \).
2. \( -7(2y + 11) - 2y = -13 \).
3. \( -14y - 77 - 2y = -13 \).
4. \( -16y - 77 = -13 \).
5. \( -16 = 64 \).
6. \( y = -4 \).
7. \( x + 8 = 11 \).
8. \( x = 3 \).
9. \( (3, -4) \).

Ensure the steps are coherent with the substitution method to solve the system.

Answer 2

are you sure

Answer 3

Let’s clarify and ensure that we correctly outline the steps taken to solve the system of equations by substitution. I apologize for any confusion earlier. Here’s a detailed breakdown of the process to solve the equations:

Given equations:

1. \( -7x - 2y = -13 \) (Equation 1)
2. \( x - 2y = 11 \) (Equation 2)

Steps to solve by substitution:

1. Rearrange Equation 2 to solve for \( x \): \[ x - 2y = 11 \implies x = 2y + 11 \]

2. Substitute \( x \) in Equation 1: Replace \( x \) in Equation 1 with \( (2y + 11) \): \[ -7(2y + 11) - 2y = -13 \]

3. Distribute \(-7\): \[ -14y - 77 - 2y = -13 \]

4. Combine like terms: \[ -16y - 77 = -13 \]

5. Add 77 to both sides: \[ -16y = 64 \]

6. Divide by -16: \[ y = -4 \]

7. Substitute \( y = -4 \) back into Equation 2 to find \( x \): \[ x - 2(-4) = 11 \implies x + 8 = 11 \]

8. Solve for \( x \): \[ x = 3 \]

9. Final answer: The solution to the system is \( (3, -4) \).

Ordered Steps Based on Your Original Choices:

Putting together the information from the breakdown:

1. From Equation 2: \( x - 2y = 11 \) → \( x = 2y + 11 \)
2. Substituting: \( -7(2y + 11) - 2y = -13 \)
3. Distributing: \( -14y - 77 - 2y = -13 \)
4. Combining: \( -16y - 77 = -13 \)
5. Adding 77: \( -16y = 64 \)
6. Dividing: \( y = -4 \)
7. Substituting back into Equation 2: \( x + 8 = 11 \)
8. Solving for \( x \): \( x = 3 \)
9. Solution: \( (3, -4) \)

If a specific option from your provided choices aligns with these steps, that would be the correct order. Thank you for your patience, and let me know if you have any more questions!