B C
Statement
Reason
1. AB =
- 露
given
2
✓
3.
AD + DB
DB
CE + EB
EB
using common denominators
4
AB = AD + DB
CB = CE + EB
segment addition
5. AB = B
6. ZABC - ZDBE
7. AABC ADBE
Substitution Property of Equality
Reflexive Property of Congruence
SAS criterion for similarity
Corresponding angles of similar triangles are congruent.
If the corresponding angles formed by two lines intersected by a transversal are
congruent, then the lines are parallel.
8. Z BAC = 2BDE
9. DEAC

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step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1