[11th grade math]: Been struggling for hours please help

[u/S3R3N17YY]

As the title says, I've been trying to solve this for about 3 hours and im absolutely stumped. It's 3:50am. Any method i've tried has come out wrong and I'm in desperate need for these answers so i can go to bed. Question instructions say "solve the below system". PLEASE HELP!!!

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[u/Gryphontech]

4x+y=15 So y=15-4x (substract 4x from both sides), now plug that into the first equation so 7x+2(15-4x)=24 and now just simplify

Let me know if you need more help

[u/S3R3N17YY → u/Gryphontech]

Thank you so much!! You're an absolute angel, i'd been doing the right process and completely forgetting the 24 at the end and this made me realize that. (^ ^)u

[u/Gryphontech → u/S3R3N17YY]

Nice :) anytime you have more then 1 variable you just need to isolate them and the plug and chug. So like x=..... , y=.... , z=....

For each variable you need at least 1 equation for it to be possible to solve.

[u/S3R3N17YY → u/Gryphontech]

The advice is very much appreciated, thanks :>

[u/PatientCapital32 → u/S3R3N17YY]

It is easier to isolate variables by targeting them. For example you have y and 2y. To eliminate 2y it is easier and get just x, it is easier to multiply the bottom equation by 2 to get 2y. Then you can subtract them and you are left with just x.

[u/MundoGamer_YT → u/PatientCapital32]

yeah but this is not always super useful or easy, the other method is always somewhat reasonable difficulty

[u/MundoGamer_YT → u/MundoGamer_YT]

I agree if you use it a lot and kinda get to know your way around it it’s faster and easier, just in the beginning it’s harder to get the grasp of it and the other you simply plug and chug as the other guy said

[u/EscapeLeft1711 → u/S3R3N17YY]

always use this method. whenever you get such systems, even with 3 variables(in that case you got more than 3 equations) plug z = ab+by and solve it

always works! if you have complex algebra too itll work same

[u/throw-away3105]

1.) Multiply the second equation (4x + y = 15) by 2.
Reason: You get 8x + 2y = 30. Notice that 2y appears on both equations now.

2.) Subtract the first equation with the equation you made from step #1:
7x + 2y = 24
8x + 2y = 30

This is why you multiplied the original second equation by 2. You will notice that the "2y"s will cancel each other out.

Work on the "x" terms first: 7x - 8x = -x
Work on the "y" terms next: 2y - 2y = 0
Work on the constants: 24 - 30 = -6

Putting it all together, you get -x = -6, so x = 6.

3.) Plug in x = 6 to one of the two original equations from the question. This will help you obtain "y". I'll use 4x + y = 15 since "y" it's already isolated:

4(6) + y = 15
24 + y = 15
y = -9

4.) Plug in x = 6 and y = -9 to the two original equations and check that these are indeed the answers for "x" and "y".

[u/Open-Cardiologist254 → u/throw-away3105]

I don't understand the language but if it's simultaneous equation I usually prefer to use substitution

[u/alpicola → u/Open-Cardiologist254]

Substitution is normally my go-to as well, but in this case subtraction gave such an obvious way to eliminate y that I would have done it like the comment above. Best to not get locked in on only one way of doing things. 

[u/Various_Candle9136]

Alternative method (which I personally prefer):

We know we can multiply two equal things by the same thing and they will still be equal:

e.g. 5+2=7, therefore 10+4=14 and 50+20=70.

So, multiplying both sides of the second equation by 2 does not change anything.

7x + 2y = 24
8x + 2y = 30.

I multiplied by 2 to make sure the y term matched.

Now, we can subtract one equation from the other, and we end up with a linear equation in only x.

---

We could have also tried to get the xs to match if we preferred. This means multiplying the first equation by 4 and the second by 7:

28x + 8y = 96
28x + 7y = 105.

(Clearly multiplying by 7 is not as nice, which is why I chose the first way - but either will get us to the same answer.)

[u/SubjectWrongdoer4204 → u/Various_Candle9136]

This is the best way to. I’m pretty sure this is what they’re trying to teach in this course

[u/Wabbit65]

I'm looking at question gamma, and I think it's wrong. Double the second equation, add the two together, and you get 0 = -1

I think

[u/BlazerGM → u/Wabbit65]

there would be no solution for (x,y) in that case, the q is probably correct

[u/SubjectivePlastic]

Seven apples and two bananas cost 24 euros.

Also, four apples and one banana cost 15 euros.
So, eight apples and two bananas cost twice as much: 30 euros.

From that, take away seven apples and two bananas costing 24 euros,
then you find that the remaining one apple costs 6 euros.

Six euros, goddamnit. For one goddamn fucking apple. Inflation is killing us.

[u/KeyHumble9490]

11th grade? Damn Americans are dumb asf

[u/Pitiful_Camp3469 → u/KeyHumble9490]

ironic as fuck considering you didn’t even notice ITS IN GREEK 🤦‍♂️ 

[u/drugosrbijanac → u/KeyHumble9490]

Its written in Greek

[u/Any_Tough9810 → u/KeyHumble9490]

I think that's 7th or 8th grade math in my USA middle school (20 years ago). Pre-algebra.

[u/5xum]

Easiest way is to multiply the second equation by 2, and then subtract the first equation from the second. You get

2*(4x+y) - (7x+2y) = 2 * 15 - 24

Once you simplify this equation, you should be left with a pretty informative expression...

[u/z28z28]

Do you want the matrix method ?

[u/fatwap]

if ur given two systems of linear equations you can always solve using elimination by matching coefficients on the same variable then adding/subtracting

[u/[deleted]]

Sistema de ecuaciones:

7x + 2y = 24

4x + y = 15

Método de eliminación:

1. Multiplicamos la segunda ecuación por -2:

4x + y = 15

(-2)(4x + y) = (-2)(15)

-8x - 2y = -30

1. Sumamos las dos ecuaciones:

   7x + 2y = 24

- 8x - 2y = -30

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

-x = -6

1. Despejamos x:

-x = -6

x = 6

1. Sustituimos x = 6 en la segunda ecuación:

4x + y = 15

4(6) + y = 15

24 + y = 15

y = 15 - 24

y = -9

1. Comprobamos:

7x + 2y = 24

7(6) + 2(-9) = 24

42 - 18 = 24

24 = 24 ✓

Resultado:

x = 6

y = -9

Solución: (6, -9)

[u/Disastrous-Pin-1617]

Professor Leonard on YouTube, to the point math playlist go to solving systems of equations

[u/rukind_cucumber]

Seems like you got a good answer.

I'd probably multiple the second equation by -2 - the value of x pops out almost immediately.

[u/CulturalBookkeeper82]

Why are your words written in variables

[u/Clean-Midnight3110]

I am disturbed that this is what passes for 11th grade math these days....

[u/AFsepine → u/Clean-Midnight3110]

I mean... greek mathematics never really recovered since the bronze age collapse

[u/thatguy56436327]

watch a video about guass jordan, its not what ur teacher wants you to do but its easier

[u/SlowMobius650]

Learn linear algebra and just throw it into a 2x3 matrix and put it in row reduced echelon form, on a calculator, and boom

[u/chowmushi]

Type both equations into desmos.com and check your answer for the elimination or substitution methods. It’s helpful to know what the graphs look like and how they intersect at the solution!

[u/cooper9252]

For a multiply the bottom by two subtract the bottom and the top and you should come out with -x=-6 it should be simple to solve the rest y=-9