Put the steps in order that are used to solve the following systems of equations by substitution.

Question

−7x−2y=−13

x−2y=11

== 3

= y =- 4

= -7(2y+11)-2y =- 13

= x-2(-4)=11

= -16y =64

= -16y-77 =- 13

= x-2y=11->x=2y+11

= (3,-4)

= x+8=11

= -14y-77-2y =- 13

Answer 1

To solve the given systems of equations by substitution, let's put the steps in a logical order:

1. Rewrite one of the equations to express one variable in terms of the other:
   \( x - 2y = 11 \) → \( x = 2y + 11 \)

2. Substitute this expression into the other equation to eliminate one variable:
   Substitute \( x = 2y + 11 \) into the equation \( -7x - 2y = -13 \)
   \( -7(2y + 11) - 2y = -13 \)

3. Expand and simplify the substituted equation:
   \( -14y - 77 - 2y = -13 \) → Combine like terms
   \( -16y - 77 = -13 \)

4. Isolate the variable:
   Add 77 to both sides:
   \( -16y = 64 \)
   Divide by -16:
   \( y = -4 \)

5. Substitute the value of \( y \) back into the expression for \( x \):
   \( x = 2(-4) + 11 \)
   \( x = -8 + 11 \)
   \( x = 3 \)

6. Identify the solution:
   So, the solution is \( (x, y) = (3, -4) \)

The correct order of the steps is:

1. \( x - 2y = 11 \) → \( x = 2y + 11 \)
2. Substitute: \( -7(2y + 11) - 2y = -13 \)
3. Expand: \( -14y - 77 - 2y = -13 \)
4. Combine: \( -16y - 77 = -13 \)
5. Isolate: \( -16y = 64 \)
6. Solve for \( y \): \( y = -4 \)
7. Substitute \( y \) back: \( x = 2(-4) + 11 \)
8. Find \( x \): \( x = 3 \)
9. Solution: \( (3, -4) \)

Answer 2

x+8=11?

Answer 3

The equation \(x + 8 = 11\) doesn't seem directly relevant to the steps for solving the original system of equations by substitution. However, let's examine how it might be related:

If you solve \(x + 8 = 11\), you would isolate \(x\) by subtracting 8 from both sides:

1. \(x + 8 = 11\)
2. Subtract 8 from both sides:
   \(x = 11 - 8\)
3. \(x = 3\)

This result \(x = 3\) is indeed consistent with the final solution of the system of equations given earlier, where we found that \(x = 3\) and \(y = -4\).

In the context of solving the equations you initially provided, \(x + 8 = 11\) can be viewed as a step that might emerge from a similar solving process, but it isn't a step I included because it doesn't arise directly from the equations being solved.

If you have a specific reason for mentioning \(x + 8 = 11\) or if it's part of another problem, please provide more context, and I'd be happy to help further!

Answer 4

where do i put x+8=11

Answer 5

To incorporate the equation \(x + 8 = 11\) into the process of solving the system of equations you provided by substitution, it would likely be placed after isolating the variable \(x\) in one of your original equations.

Here's how it might fit into the steps:

1. Rewrite one of the equations to express one variable in terms of the other:
   From \(x - 2y = 11\), we can rearrange it to:
   \(x = 2y + 11\)

2. Substitute this expression into the other equation to eliminate one variable. Substitute \(x = 2y + 11\) into the equation:
   \(-7x - 2y = -13\)
   becomes: \(-7(2y + 11) - 2y = -13\)

3. Expand and simplify the substituted equation:
   \(-14y - 77 - 2y = -13\) → Combine like terms:
   \(-16y - 77 = -13\)

4. Isolate the variable:
   Add 77 to both sides:
   \(-16y = 64\)
   Divide by -16:
   \(y = -4\)

5. Substitute the value of \(y\) back into the expression for \(x\):
   Now we substitute \(y = -4\) back into \(x = 2y + 11\):
   \(x = 2(-4) + 11\)

6. Simplify that expression:
   Here, you have:
   \(x = -8 + 11\)
   \(x = 3\)

7. Verify with \(x + 8 = 11\):
   This step is ultimately just verifying that \(x = 3\) satisfies \(x + 8 = 11\):
   \(3 + 8 = 11\)

8. Identify the solution:
   Thus, the final solution is \((x, y) = (3, -4)\).

So to answer your question, you can include \(x + 8 = 11\) as a verification step to confirm that \(x = 3\) is correct, though it does not directly form part of the substitution method in solving the system of equations.