Question

Put the steps in order that are used to solve the following systems of equations by substitution.
-7x-2y=-13
х - 2y = 11

=x-2(-1) =11
Mark as Complete
=-16y-77=-13
=-14y-77-2y=-13
=x- 2y=11 -> x=2y+11
=-7(2y+11) - 2y=-13
= (3, -4)
=x =3
= - 16y = 64
=x+8=11
=y=-4

Answer 1

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

1. **Start with the original equations:**
-7x - 2y = -13
x - 2y = 11

2. **Solve one of the equations for one variable. In this case, we'll solve x from the second equation:**
\( x - 2y = 11 \) -> \( x = 2y + 11 \)

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

4. **Distribute and simplify:**
\( -14y - 77 - 2y = -13 \)
Combine like terms:
\( -16y - 77 = -13 \)

5. **Solve for y:**
Add 77 to both sides:
\( -16y = 64 \)
Divide by -16:
\( y = -4 \)

6. **Now substitute the value of y back into the equation for x:**
\( x = 2(-4) + 11 \)
\( x = -8 + 11 \)
\( x = 3 \)

7. **The final solution is:**
\( (x, y) = (3, -4) \)

Thus, the ordered steps in solving the system by substitution are:

1. \( x - 2y = 11 \) -> \( x = 2y + 11 \)
2. Substitute: \( -7(2y + 11) - 2y = -13 \)
3. \( -14y - 77 = -13 \)
4. \( -16y = 64 \)
5. \( y = -4 \)
6. Substitute back to find x: \( x = 3 \)
7. Solution: \( (3, -4) \)