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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) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

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

7 answers

To solve the system of equations by substitution, you can follow these steps in order:

  1. Start with the equation in simpler form:

    • x - 2y = 11

  2. Solve for x in terms of y:

    • x = 2y + 11

  3. Substitute x in the first equation:

    • Substitute x = 2y + 11 into the first equation:
    • -7(2y + 11) - 2y = -13

  4. Simplify the equation:

    • -14y - 77 = -13

  5. Solve for y:

    • -14y = 64
    • y = -4

  6. Substitute y back into expression for x:

    • x = 2(-4) + 11
    • x = 3

  7. Write the solution as a coordinate pair:

    • (3, -4)

Putting these in order yields the following sequence:

  1. x - 2y = 11 → x = 2y + 11
  2. Substitute into the first equation: -7(2y + 11) - 2y = -13
  3. -14y - 77 = -13
  4. -14y = 64
  5. y = -4
  6. Substitute back to find x: x = 2(-4) + 11
  7. x = 3
  8. Solution: (3, -4)

The correct order of steps to solve the system of equations is:

  1. x - 2y = 11 → x = 2y + 11
  2. -7(2y + 11) - 2y = -13
  3. -14y - 77 = -13
  4. -14y = 64
  5. y = -4
  6. x = 3
  7. (3, -4)
i need all 10 steps

I apologize for not providing the exact number of steps. Here’s the complete ten-step process for solving the system of equations by substitution, filling in all necessary details for clarity:

  1. Start with the given system of equations:

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

  2. Rearrange Equation 2 to express x in terms of y:

    • \(x = 2y + 11\)

  3. Substitute the expression for x from Equation 2 into Equation 1:

    • Substitute \(x = 2y + 11\) into \(-7x - 2y = -13\)
    • This gives: \(-7(2y + 11) - 2y = -13\)

  4. Distribute \(-7\) in the equation:

    • \(-14y - 77 - 2y = -13\)

  5. Combine like terms:

    • \(-16y - 77 = -13\)

  6. Isolate the variable term by adding 77 to both sides:

    • \(-16y = 64\)

  7. Solve for y by dividing both sides by -16:

    • \(y = -4\)

  8. Substitute the value of y back into the equation for x:

    • Substitute \(y = -4\) into \(x = 2y + 11\)
    • \(x = 2(-4) + 11\)

  9. Calculate the value of x:

    • \(x = -8 + 11\)
    • \(x = 3\)

  10. Present the solution as an ordered pair (x, y):

  • The solution is \((3, -4)\)

This detailed breakdown covers all the necessary steps to solve the system of equations by substitution.

answer it with the option i gave you to choose from

Sure! Based on the answer choices you provided, here are the steps arranged in the correct order for solving the system of equations using substitution:

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

These steps match the process for solving the system of equations by substitution, in the proper order, using your provided choices.

answer it with the choices i gave you in 10 steps

I apologize for the misunderstanding. Here are the steps organized using the specific choices you provided, filled in to create a full 10-step process:

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

Now, I will reorganize your specific answer choices to match a complete 10-step process:

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

Now let's fill in additional placeholders for the extra steps to make it 10:

  1. \( x - 2y = 11 \) → \( x = 2y + 11 \)
  2. Substitute into first equation: \( -7(2y + 11) - 2y = -13 \)
  3. Expand: \( -14y - 77 = -13 \)
  4. Combine: \( -14y - 77 = -13 \)
  5. Isolate: \( -16y = 64 \)
  6. Solve for y: \( y = -4 \)
  7. Substitute back into x: \( x - 2(-4) = 11 \)
  8. Solve for x: \( x = 3 \)
  9. Write the solution: \( (3, -4) \)
  10. Verify solution with original equations (not provided in your list but usually a good practice).

So here it is using your response options (note that response item 3 is repeated as it appears twice, but only once can be justified):

  1. \( x - 2y = 11 \) → \( x = 2y + 11 \)
  2. \( -7(2y + 11) - 2y = -13 \)
  3. \( -14y - 77 = -13 \)
  4. \( -14y - 77 = -13 \)
  5. \( -16y = 64 \)
  6. \( y = -4 \)
  7. \( x - 2(-4) = 11 \)
  8. \( x = 3 \)
  9. \( (3, -4) \)
  10. Verify solution (not given in the choices).

I hope this aligns better with your request! If you need further clarification, feel free to let me know.