Put the steps in order that are used to solve the following system of equations by substitution. --> -7x-2y=-13 (this next part is below it but is not a fraction) x-2y=11 steps that need to be put in order: -16y=64, y=-4, x+8=11, -14y-77-2y=-13, -16y-77=-13, -7(2y+11)-2y-13 , x-3, x-2y=11->x=2y+11, (3,4),

Question

x-2(-4)=11

Answer 1

To solve the system of equations using substitution, we can outline the steps clearly. Here are the given equations:

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

To solve by substitution, we will first solve one of the equations for one variable and then substitute that expression into the other equation.

Here are the given steps arranged in the correct order for solving the system:

1. Start with the second equation:
   \(x - 2y = 11\)

2. Solve for \(x\):
   \(x = 2y + 11\)

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

4. Distribute and simplify:
   \(-14y - 77 - 2y = -13\)

5. Combine like terms:
   \(-16y - 77 = -13\)

6. Add 77 to both sides:
   \(-16y = 64\)

7. Divide by -16:
   \(y = -4\)

8. Substitute \(y\) back into the equation for \(x\):
   \(x - 2(-4) = 11\)

9. Solve for \(x\):
   \(x + 8 = 11\)

10. Subtract 8 from both sides:
    \(x = 3\)

11. Final solution (3, -4):
    (3, -4)

Now let's list out the individual steps you provided in chronological order following the process outlined above:

1. \(x - 2y = 11 \rightarrow x = 2y + 11\)
2. \(x = 2y + 11\)
3. \(-7(2y + 11) - 2y = -13\)
4. \(-14y - 77 - 2y = -13\)
5. \(-16y - 77 = -13\)
6. \(-16y = 64\)
7. \(y = -4\)
8. \(x + 8 = 11\)
9. \(x = 3\)
10. \((3, -4)\)

Thus, the ordered steps are:

• \(x - 2y = 11 \rightarrow x = 2y + 11\)
• \(-7(2y + 11) - 2y = -13\)
• \(-14y - 77 - 2y = -13\)
• \(-16y - 77 = -13\)
• \(-16y = 64\)
• \(y = -4\)
• \(x + 8 = 11\)
• \(x = 3\)
• \((3, -4)\)