# [SOLVED] 2 Substitution Problems

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• Aug 12th 2009, 06:08 PM
WeezerGamez
[SOLVED] 2 System Problems
Hello everyone, I am doing some Algebra 2 work and I have two system equation problems that I am stuck on from a worksheet.

"SOLVE SYSTEM EQUATION:"

Here is the first one that I am stuck on:

Y = 3X + 1
Y = 3X + 5

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Here is the second one:

Y = 7 - 2X
2X + Y = 7

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

Thank you in advance, I appreciate any help given.
• Aug 12th 2009, 06:30 PM
skeeter
Quote:

Originally Posted by WeezerGamez
Hello everyone, I am doing some Algebra 2 work and I have two substitution problems that I am stuck on from a worksheet.

"SOLVE EACH BY SUBSTITUTION:"

Here is the first one that I am stuck on:

Y = 3X + 1
Y = 3X + 5

3x+1 = 3x+5

subtract 3x from both sides

1 = 5 ... what does this tell you?

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

Here is the second one:

Y = 7 - 2X
2X + Y = 7

2x + (7 - 2x) = 7

7 = 7 ... what does this tell you?

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

...
• Aug 12th 2009, 06:37 PM
pickslides
Quote:

Originally Posted by WeezerGamez
"SOLVE EACH BY SUBSTITUTION:"

Here is the first one that I am stuck on:

Y = 3X + 1
Y = 3X + 5

Hi WeezerGamez the problem with the system of equations you have posted is that is has no solution. Therefore it can't be solved. The reason for this is each equation has a gradient of 3. This means they do not meet, they are parallel, just like train tracks.
• Aug 12th 2009, 06:41 PM
WeezerGamez
I thank you both for your replies... I really appreciate the help.

If the system that I posted does not have a solution, can you explain to me what the work is that Skeeter did in the previous post? Is the work hes done so far correct? I mean, since I have to show work to show that there is no solution, I can't just write that there isn't one, is the work that was posted in the previous post sufficient enough as is to copy down? Thank you.
• Aug 12th 2009, 06:55 PM
pickslides
Skeeter's work is sufficent to show in explaining there are no solutions.

Skeeter's work ends with an equation that either makes no sense 1 = 5 or tells you nothing about the system 7 = 7.
• Aug 13th 2009, 04:33 AM
jgv115
haha how can Y= 3X + 5 AND 3X + 1
• Aug 13th 2009, 05:53 AM
skeeter
Quote:

Originally Posted by WeezerGamez
I thank you both for your replies... I really appreciate the help.

If the system that I posted does not have a solution, can you explain to me what the work is that Skeeter did in the previous post? Is the work hes done so far correct? I mean, since I have to show work to show that there is no solution, I can't just write that there isn't one, is the work that was posted in the previous post sufficient enough as is to copy down? Thank you.

A system of two linear equations may behave in any one of three possible ways:

1. The system has infinitely many solutions.
2. The system has a single unique solution.
3. The system has no solution.

the conclusion that 1 = 5 tells you there is no solution, and as stated by pickslides, the two equations represent parallel lines.

the conclusion 7 = 7 tells you the two equations represent the same line, and that there exists an infinite number of solutions.