Question

Show all work. Solve for x and y.

Answer 1

Greetings!

Using the Parallel Line Theorem (c-formation), we can conclude that:

`(5z+21)+(3z-11)=180`

Combine like terms:

`5z+21+3z-11=180`


`8z+10=180`

Add -10 to both sides:

`(8z+10)+(-10)=(180)+(-10)`


`8z=170`

Divide both sides by 8:

`(8z)/(8)= (170)/(8)`


`\boxed{z=(85)/(4)}`

Using the Parallel Line Theorem (z-formation), we can also conclude that:

`(3z-11)=y`

Input the value for z:

`(3((85)/(4))-11)=y`

Combine like terms:

`((255)/(4))-11=y`


`(255)/(4)-(44)/(4)=y`


`(211)/(4)=y`


`\boxed{y=(211)/(4)}`


Lastly, using the Parallel Line Theorem (f-formation), we can conclude that:

`y=(7x+7)`

Input the value for y:

`(211)/(4)=(7x+7)`

Add -7 to both sides:

`((211)/(4))+(-7)=(7x+7)+(-7)`


`(211)/(4)-(28)/(4)=7x`


`(183)/(4)=7x`

Divide both sides by 7:

`((183)/(4))/(7)= (7x)/(7)`


`((183)/(4))((1)/(7))=x`


`((183)/(28))=x`


`\boxed{x=(183)/(28)}`

The Solution Is:

`\boxed{(183)/(28),(211)/(4),(85)/(4)}`

I hope this helped!
-Benjamin