Proving Vertical Angles Are Congruent CI
Given: 22 and 24 are vertical angles.
Prove: L2 - 24
Statements Reasons
m2 + m2.3 = 180
mZ3+ m24 = 180
22 and 24 are vert, angles
x
22 and 23 are a linear pair
23 and 24 are a linear pair
lines m and n intersect at P
m
1
Statements
Reasons
2
р
n
4
tary
3
gary
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
otebo
Intro
covery

{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

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0