Solve the system using the addition method

[flora33]

Hello again all! I've got one using the addition method that appears right, then I perform my check and the answers do not match up...

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2

First I multiplied the -7x + y = 8 by 2:
-7x * 2 + y * 2= 8 * 2
-14x + 2y = 16

I then multiplied 2x – y = 2 by 7:
2x * 7 – y * 7 = 2 * 7
14x - 7y = 14

So now I have both equations with the coeffecient of x only differing by opposite signs, so then I do the addition:
-14x + 2y = 16
14x - 7y = 14

The x terms drop out:
-5y = 30

Solve for y:
-5y/5 and 30/5
y = 6

Then substitute y = 6 for x in 2x - y = 2
2x - 6 = 2
2x - 6 + 6 = 2 + 6
2x = 8
2x/2 and 8/2
x = 4

So my solution is (4,6) but when I check:
-7x + y = 8
-7(4) + 6 = 8
-28 + 6 = -22
-22 = 8

2x - y = 2
2(4) - 6 = 2
8 - 6 = 2
2 = 2

Since they both don't check, there is something wrong some where, right? I was excited that I had this one right until I got to the end!
:x

 

[Deleted member 4993]

Hello again all! I've got one using the addition method that appears right, then I perform my check and the answers do not match up...

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2

First I multiplied the -7x + y = 8 by 2:
-7x * 2 + y * 2= 8 * 2
-14x + 2y = 16

I then multiplied 2x – y = 2 by 7:
2x * 7 – y * 7 = 2 * 7
14x - 7y = 14

So now I have both equations with the coeffecient of x only differing by opposite signs, so then I do the addition:
-14x + 2y = 16
14x - 7y = 14

The x terms drop out:
-5y = 30<<<<< This should give you y = -6

and correspondingly

x = -2

However, you have done an exceptional job at showing your work - that made my work very easy. If I were grading your paper, I would have given you 90-95% points - specially after showing that there was something wrong your work. Keep up the good work.
Solve for y:
-5y/5 and 30/5
y = 6

Then substitute y = 6 for x in 2x - y = 2
2x - 6 = 2
2x - 6 + 6 = 2 + 6
2x = 8
2x/2 and 8/2
x = 4

So my solution is (4,6) but when I check:
-7x + y = 8
-7(4) + 6 = 8
-28 + 6 = -22
-22 = 8

2x - y = 2
2(4) - 6 = 2
8 - 6 = 2
2 = 2

Since they both don't check, there is something wrong some where, right? I was excited that I had this one right until I got to the end!
:x

 

[flora33]

Hello again all! I've got one using the addition method that appears right, then I perform my check and the answers do not match up...

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2

First I multiplied the -7x + y = 8 by 2:
-7x * 2 + y * 2= 8 * 2
-14x + 2y = 16

I then multiplied 2x – y = 2 by 7:
2x * 7 – y * 7 = 2 * 7
14x - 7y = 14

So now I have both equations with the coeffecient of x only differing by opposite signs, so then I do the addition:
-14x + 2y = 16
14x - 7y = 14

The x terms drop out:
-5y = 30<<<<< This should give you y = -6

and correspondingly

x = -2

However, you have done an exceptional job at showing your work - that made my work very easy. If I were grading your paper, I would have given you 90-95% points - specially after showing that there was something wrong your work. Keep up the good work.
Solve for y:
-5y/5 and 30/5
y = 6

Then substitute y = 6 for x in 2x - y = 2
2x - 6 = 2
2x - 6 + 6 = 2 + 6
2x = 8
2x/2 and 8/2
x = 4

So my solution is (4,6) but when I check:
-7x + y = 8
-7(4) + 6 = 8
-28 + 6 = -22
-22 = 8

2x - y = 2
2(4) - 6 = 2
8 - 6 = 2
2 = 2

Since they both don't check, there is something wrong some where, right? I was excited that I had this one right until I got to the end!
:x

Subhotosh,

Thanks so much! I appreciate that. Too bad you aren't my teacher! I get so much help from you and others here, I definitely don't think I would understand a lot of this stuff if I didn't have the discussion board!

I see where I made my error- again with those "+" and "-" signs. They always get me!
Thanks again!
Flora

 

[Mrspi]

Hello again all! I've got one using the addition method that appears right, then I perform my check and the answers do not match up...

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2

You could have made much less work for yourself if you had noted that the coefficients of the y terms are ALREADY opposites. If you add the two equations together, you'll eliminate y:

-7x + y = 8
2x - y = 2
-------------
-5x = 10

Then, divide both sides by -5....and be VERY careful about your signs.


First I multiplied the -7x + y = 8 by 2:
-7x * 2 + y * 2= 8 * 2
-14x + 2y = 16

I then multiplied 2x – y = 2 by 7:
2x * 7 – y * 7 = 2 * 7
14x - 7y = 14

So now I have both equations with the coeffecient of x only differing by opposite signs, so then I do the addition:
-14x + 2y = 16
14x - 7y = 14

The x terms drop out:
-5y = 30

Solve for y:
-5y/5 and 30/5
y = 6

Then substitute y = 6 for x in 2x - y = 2
2x - 6 = 2
2x - 6 + 6 = 2 + 6
2x = 8
2x/2 and 8/2
x = 4

So my solution is (4,6) but when I check:
-7x + y = 8
-7(4) + 6 = 8
-28 + 6 = -22
-22 = 8

2x - y = 2
2(4) - 6 = 2
8 - 6 = 2
2 = 2

Since they both don't check, there is something wrong some where, right? I was excited that I had this one right until I got to the end!
:x

 

[flora33]

Hello again all! I've got one using the addition method that appears right, then I perform my check and the answers do not match up...

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2

You could have made much less work for yourself if you had noted that the coefficients of the y terms are ALREADY opposites. If you add the two equations together, you'll eliminate y:

-7x + y = 8
2x - y = 2
-------------
-5x = 10

Then, divide both sides by -5....and be VERY careful about your signs.


First I multiplied the -7x + y = 8 by 2:
-7x * 2 + y * 2= 8 * 2
-14x + 2y = 16

I then multiplied 2x – y = 2 by 7:
2x * 7 – y * 7 = 2 * 7
14x - 7y = 14

So now I have both equations with the coeffecient of x only differing by opposite signs, so then I do the addition:
-14x + 2y = 16
14x - 7y = 14

The x terms drop out:
-5y = 30

Solve for y:
-5y/5 and 30/5
y = 6

Then substitute y = 6 for x in 2x - y = 2
2x - 6 = 2
2x - 6 + 6 = 2 + 6
2x = 8
2x/2 and 8/2
x = 4

So my solution is (4,6) but when I check:
-7x + y = 8
-7(4) + 6 = 8
-28 + 6 = -22
-22 = 8

2x - y = 2
2(4) - 6 = 2
8 - 6 = 2
2 = 2

Since they both don't check, there is something wrong some where, right? I was excited that I had this one right until I got to the end!
:x

You're right. Good point! Thanks for the tip. Yes, I know I must watch those signs!!!

Flora