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# Worked example: non-equivalent systems of equations

Sal analyzes a couple of systems of equations and determines whether they have the same solution as a third given system.

## Want to join the conversation?

• At , how did you get y = 2x - 1? • Sal started with the equation: 14x - 7y = 7
He then subtracted 14x from both sides, creating: -7y = -14x + 7
Then, he divide the equation by -7. I'll write it out so you can see the steps:
-7y/(-7) = -14x/(-7) + 7/(-7)
y = 2x - 1
Hope this helps.
• wouldn't hansel's 2nd equation be equivalent to the teacher's 2nd equation divided by -7? • How do we graph non linear equations and solve. • So if scarlett's system of equation is NOT equivalent to the teacher's system of equation, How would Sal know that Hansol's system of equation is NOT equivalent to the teacher's system of equation if he didn't graph them like what he did in Scarlett's? • Hansol had the same problem that Scarlett did, being that the lines were parallel. The way you can tell is that both Scarlett's and Hansol's right hand side was different from the teachers right hand side, while the left hand sides were the same. The mistake that they both made is that they forgot the golden rule of algebra, which is whatever you do to one side of an equation, you MUST do to the other side.
• "the ratio
between x and y is the same,
the constant term is going to be different.
And I would make the claim
that this alone tells you that Scarlett's system
is not equivalent to the teacher.
" at

I suspect this is not valid reasoning. I guess the correct statement is:
"this alone tells you that Scarlett's 2nd equation
is not equivalent to teacher's 2nd equation.
"
Am I right? • What's the difference between substitution and elimination for the systems of equations? • At -, sal said "I would make a claim that this alone tells you that Scarlett's system of equations is NOT equivalent to the teacher?" What does Sal mean when he said "this alone"? • To have an equivalent system, you must have equivalent equation. Sal points out on the 2nd equations that the left sides match, but the right sides do not match. So, the equations can't be equivalent. The phrase "this alone" is referring to the fact that the 2 sides of the equations do not match. It is basically all the info you need to determine that the system is not equivalent to the original.

Hope this helps.
• I have seen a system like this in the practice exercise for the Teacher:
14x-7y=-28
-8x+4y=15
If I try to apply the elimination method I finally get 0 = -1.75. The question was if the equations of the other students are equivalent and one of them actually had the same weird result so they were equivalent. But I presume the exercise is wrong cause that equivalence doesn't make any sense.
(1 vote) • Good observation. Let us rearrange our equations and see what happens:
𝑦 = 2𝑥 + 4
𝑦 = 2𝑥 + (15/4)
Notice that these are both linear equations meaning they graph lines. Also note that they both have a slope of 2. These means that both lines are parallel. However, both lines have different 𝑦-intercepts. Combining these two facts, we know that the two lines never intersect. This means for this system of equations, there are no solutions which explains the nonsensical results you were getting. Comment if you have any questions.  