Question

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

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

=-16y-77=-13

=x- 2(-4) = 11

=y=-4

= - 16y = 64

= x+8=11

= x =3

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

= (3, -4)

Answer 1

To solve the given system of equations using the substitution method, we can arrange the steps in the correct order:

1. \( x - 2y = 11 \) → \( x = 2y + 11 \) (Isolate x)

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

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

8. Simplify:
\( x + 8 = 11\)

9. Solve for \( x \):
\( x = 3\)

10. Write the solution as an ordered pair:
\( (3, -4) \)

So the ordered sequence is:
1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → 10.