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".

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