Solve each of the following systems by substitution
20. 8x - 4y = 16
y = 2x - 4
----------------------------------------------------------------------------------------------------------------
28. 4x - 12y =5
-x + 3y = -1

Solve each of the following systems by using either addition or substitution. If a unique solution
does not exist, state whether the system is dependent or inconsistent.
38. 10x + 2y = 7
Y= -5x + 3

----------------------------------------------------------------------------------------------------------------
56. Social science. In a town election, the winning candidate had 220 more votes
than the loser. If 810 votes were cast in all, how many votes did each candidate
receive?

Solve each of the following systems by substitution 20. 8x - 4y = 16 y = 2x - 4

Plug the second equation into the first:

8x - 4(2x - 4) = 16

Distribute the 4:

8x - 8x + 16 = 16

Cancel terms:

16 = 16

This is a true statement, so there are infinite solutions. ---------------------------------------------------------------------------------------------------------------- 28. 4x - 12y =5 -x + 3y = -1

Solve the second equation for x:

-x + 3y = -1

Subtract 3y:

-x = -1 - 3y

Divide by -1:

x = 3y + 1

Plug that into the first equation:

4x - 12y = 5

4(3y + 1) - 12y = 5

Distribute:

12y + 4 - 12y = 5

Combine y's:

4 = 5

This is obviously false, so this system does NOT have a solution. It is inconsistent.

Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 38. 10x + 2y = 7 Y= -5x + 3

Using substitution, plug the second equation into the first:

10x + 2y = 7

10x + 2(-5x + 3) = 7

Distribute:

10x - 10x + 6 = 7

Combine x's:

6 = 7

This is obviously false, so this system does NOT have a solution. It is inconsistent.

-----------------------

---------------------------------------------------------------------------------------------------------------- 56. Social science. In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

We need two equations:

W + L = 810 (the total votes cast)

W = L + 220 (the winner had 220 more than the loser)

Now plug the second equation's W value into the first equation:

(L + 220) + L = 810

Combine L's:

2L + 220 = 810

Subtract 220:

2L = 590

Divide by 2:

L = 295

To find W, use the second equation:

W = 295 + 220 = 515

The winner had 515 votes, and the loser had 295 votes.

------------------------

Let me know if you have any questions. If not, thanks for pressing "Accept".

Solve each of the following systems by substitution 20. 8x - 4y = 16 y = 2x - 4

Plug the second equation into the first, for y:

8x - 4(2x - 4) = 16

Distribute the 4:

8x - 8x + 16 = 16

Cancel terms with x:

16 = 16

This is a true statement, but it does not involve the variables, so there are infinite solutions. ---------------------------------------------------------------------------------------------------------------- 28. 4x - 12y =5 -x + 3y = -1

Solve the second equation for x:

-x + 3y = -1

Subtract 3y from each side:

-x = -1 - 3y

Divide each side by -1:

x = 3y + 1

Plug that x value into the first equation, everytime you see x:

4x - 12y = 5

4(3y + 1) - 12y = 5

Distribute:

12y + 4 - 12y = 5

Combine y's:

4 = 5

This is obviously false, so this system does NOT have a solution. It is inconsistent.

Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 38. 10x + 2y = 7 Y= -5x + 3

Using substitution, plug the second equation into the first:

10x + 2y = 7

10x + 2(-5x + 3) = 7

Distribute the 2:

10x - 10x + 6 = 7

Combine the terms with x's:

6 = 7

This is obviously false, so this system does NOT have a solution. It is inconsistent.

-----------------------

---------------------------------------------------------------------------------------------------------------- 56. Social science. In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

Call the number of winning votes = W The losing votes = L

We need two equations:

W + L = 810 (the total votes cast)

W = L + 220 (the winner had 220 more than the loser)

Now plug the second equation's W value into the first equation:

(L + 220) + L = 810

Combine L's:

2L + 220 = 810

Subtract 220 from each side:

2L = 590

Divide each side by 2:

L = 295

To find W, use the second equation:

W = L + 220

W = 295 + 220 = 515

The winner had 515 votes, and the loser had 295 votes.

------------------------

Let me know if you have any further questions. Please let me know which steps, if any, to clarify. If not, thanks for pressing "Accept".

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal ...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

What Customers are Saying:

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!AlexLos Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.GPHesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.JustinKernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. EstherWoodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. RobinElkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.DianeDallas, TX

Meet The Experts:

LogicPro

Engineer

Satisfied Customers:

4925

Expert in Java C++ C C# VB Javascript Design SQL HTML