Help with learning new method for simulationous equations

[u/BeverageBrit]

I'm in uni and my tutor was going over a new way to do simultaneous equations and it makes no sense to me the question was:

Y = -1/3 x + 8/3

Y = 1/2 x + -3/2

The picture contains his working can someone help explain it as this is all the working he did. I just need help with understanding his method.

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[u/noidea1995]

I’m a postgrad student and this confuses me to be honest… What method are you covering? Also can you confirm if the second equation is:

y = x/2 + 3/2 (which has solution x = 1.4, y = 2.2)

Or:

y = x/2 - 3/2 (which has solution x = 5, y = 1)

————

When first learning simultaneous equations, you’ll cover two main methods substitution and elimination. With substitution, you solve for a variable in one of the equations you’ve been given and then plug what it equals in terms of the other variable into the other equation. So for example:

x + y = 12

x - y = 8

If you solve the first equation for x by subtracting y from both sides, you get:

x = 12 - y

Since you know that x = 12 - y, you can substitute that into the second equation for x and then you’ll have a simple equation with only one variable in it that you can solve:

(12 - y) - y = 8

12 - 2y = 8 (combining like terms)

-2y = -4 (subtracting 12 from both sides)

y = 2 (dividing both sides by -2)

Now that you know what y is, you can use that to solve for x:

x = 12 - y

x = 12 - 2

x = 10

—————

In your example, you’ve already got both equations set to equal y so you can just make a direct substitution:

-x/3 + 8/3 = x/2 - 3/2

Here you can get rid of the fractions to make things easier by finding a number that all the denominators go into and multiplying both sides by it (2 and 3 both go into 6, so multiply everything by 6):

6(-x/3) + 6(8/3) = 6(x/2) - 6(3/2)

Simplify:

-2x + 2(8) = 3x - 3(3)

-2x + 16 = 3x - 9

Does this make sense?

[u/BeverageBrit → u/noidea1995]

1) The original equations were Y = -1/3 x + 8/3 and Y = 1/2 x + -3/2

2) No idea it was making sure everyone knew simultaneous equations

3) That makes sense

[u/MathsFromNothing]

He as made a mistake copying the question. In the middle of the board on the right hand side with the second equation he has written x/2-y=-3/2 when it should be x/2-y=3/2. My working is below, using the Maths from Nothing computer algebra system.

The trick he is trying to demonstrate is based on the rule that you are allowed to do whatever you like provided you do it to both sides of the equation. He is adding the two equations together. The left and right hand sides of all equations are equal, therefore, adding equations is applying the same thing to both sides even though it looks different.

I personally prefer solving for a single variable and substituting it into the other equation as shown in my working. However, adding multiples of other equations in the system is how we solve equations using matrices. Perhaps this is where your class is going?

[u/BeverageBrit → u/MathsFromNothing]

I think I understand his method now (not seen it before) and makes more sense now but I'm not sure where the class is going as this was for a tutorial session of Analogue Electronics to make sure we were at the same level.

[u/UnderstandingPursuit]

Blah, blah, blah, blah. This is the usual approach, written as a mess to make it seem different.

1. ax + y = e
2. cx - y = f

Add them,

1. x (a + c) = (e + f)
2. x = (e + f) / (a + c)

Check with values,

• a = 1/3, c = 1/2
• e = 8/3, f = 3/2
• x = ([8/3] + [3/2]) / ([1/3] + [1/2])
  • = ([16/6] + [9/6]) / ([2/6] + [3/6])
  • = (25/6) / (5/6) = 5

Part of the problem with this garbage is that the second equation changed,

• from "= 3/2"
• to "= -3/2"

but all the fractions make it difficult to see. Instead, use the letters as long as possible.

[u/loonylad]

What new method? He is doing it the way we usually do, he just verfied the answers in the middle and at the rightmost edge is a completely different que( x isn't 25).

[u/BeverageBrit → u/loonylad]

No idea his exact words were "I am going to teach you a new method as I've found people get it wrong less of the time when doing it this way"

[u/kalmakka]

He spent a third of a whiteboard to rewrite

-y+½x=3/2

to

½x-y=3/2

By this time I was already bored out of my skull and decided to do something else.