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Show all work. Solve for x and y.

Show all work. Solve for x and y.-example-1

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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
User Adetunji
by
8.3k points

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