question on SIMULTANEOUS EQUATIONZ. (1 Viewer)

[unadultarated]

btw answer is -3.

Studying simultaenous equations and I still cant find the naswer to my question.

How do you know which variable x or y in either equation to isolate/ use for the subsitution.

 

[Kangaaroo]

You may isolate either variable, it doesn't matter. In this case, though, don't you think elimination would be better?

We can multiply the first equation through by 2, and get a new set of equations:

2x + 10y = -26 -- 1
2x - y = 7 -- 2

Subtracting 2 from 1, we have:
10y -(-y) = -26 - 7
11y = -33
y = -3

Now we have y, we can sub into equation 2 (or 1, if you prefer):
2x -(-3) = 7
2x + 3 = 7
2x = 4
x = 2

So, the answers are:
x = 2
y = -3

 

[unadultarated]

You may isolate either variable, it doesn't matter. In this case, though, don't you think elimination would be better?

Lets say I isolate y in equation 1. The answer is wrong. So there must be a way of selecting the right one.
Same for Isolating 2x in equation 2.

Also, I prefer substitution.

 

[fan96]

A system of simultaneous equations is just a set of conditions. When we solve a system like this, we're simply finding and using different equations that represent the same conditions.

Point being, whether you choose to do this step or that step first doesn't matter, because nothing you're doing actually changes the conditions or solutions of the system - it's just to make it easier for you to solve.

If you're finding inconsistencies like you've described, then either your system has no solution or you've made an arithmetic error somewhere.

(The system does have a solution)

Isolating in eq. ,



(multiplying the original by 5)

Substituting into ,

 

[unadultarated]

A system of simultaneous equations is just a set of conditions. When we solve a system like this, we're simply finding and using different equations that represent the same conditions.

Point being, whether you choose to do this step or that step first doesn't matter, because nothing you're doing actually changes the conditions or solutions of the system - it's just to make it easier for you to solve.

If you're finding inconsistencies like you've described, then either your system has no solution or you've made an arithmetic error somewhere.

(The system does have a solution)

Isolating in eq. ,



(multiplying the original by 5)

Substituting into ,

so what decision do you make when selecting what to isolate for substitution. Is it random?

 

[Kangaaroo]

so what decision do you make when selecting what to isolate for substitution. Is it random?

Well it can be either, but generally you'd simply choose the easiest one.

 

[fan96]

so what decision do you make when selecting what to isolate for substitution. Is it random?

If one of them is clearly more convenient, then pick that one.

For example, if we have the system



Then it would be smarter to eliminate by doubling the first equation.

The alternative is to multiply equation 1 by and equation 2 by ... a much harder task.

But don't worry about it too much - at the end of the day both methods get you to the same conclusion.

 

[JupiterPie]

x + 5y = -13 --- (1)
2x - y = 7 --- (2)

From eq. (2)
y = 2x - 7 --- (3)

Putting this value of y in eq. (1)
x + 5(2x -7) = -13
x +10x - 35 = -23
11x = -13+35
11x = 22
x = 22/11
x = 2 ----- (A)

Putting x = 2 in (3)
y = 2(2) - 7
y = 4 - 7
y = -3 -----(B)

 

[Roy G Biv]

so what decision do you make when selecting what to isolate for substitution. Is it random?

Doesn't matter at all Just choose whichever one you want. Once you gain experience, you'll start to gain a preference as to which you find easier, but really, it makes no difference.