# Math Help - [SOLVED] 2 Substitution Problems

1. ## [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

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Thank you in advance, I appreciate any help given.

2. 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?

------------------------------------
...

3. 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.

4. 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.

5. 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.

6. haha how can Y= 3X + 5 AND 3X + 1

7. 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.