Question

What is the value of the x variable in the solution to the following system of equations?
2x + 3y = 4
x - 2y = -5
answers choices..
2

-2

1

-1

Answer 1

Which system of equations am I supposed to use. Which lesson is this assignment from?

Answer 2

chapter 6, lesson 3.

Answer 3

Which system of equations do I use?
Substitution or Elimination!

Answer 4

Ok. I'll use substitution and I'm working on the problem right now!

Answer 5

2x + 3y=4 1st sol
x - 2y = -5 2nd sol
multiply 2nd sol by 2
and use elimination method

Answer 6

So, Kantharaj! It's easier to use the elimination process not substitution?

Answer 7

It's personal preference. I always do substitution.

Answer 8

Yeah, me too. Thanks for that, ChmE!

Answer 9

@alienababy How are you doing? did you get an answer?

Answer 10

@ChmE, im working on it. Ive got y= 14, but im looking for x. I dont know what to do now?

Answer 11

@alienbaby, you don't need my help anymore? I was almost finished with the equation!

Answer 12

my bad, @alienababy

Answer 13

@Johnjakile1998, i do! im trying to learn.

Answer 14

hold on. Your y is wrong I got 2

Answer 15

You don't have to shout! Lol. Alright, I'll put down the steps and then tell if you understand, and you can tell me.

Answer 16

@Chme. I got the same y, @alienababy it's 2!

Answer 17

im so confused. how?

Answer 18

@ChmE, do you want to explain or me?

Answer 19

@Johnjakile1998 will show the steps for the substitution and I'll show the steps for elimination

Answer 20

sounds good to me :)

Answer 21

Cool! I do better with substitution anyway! Quick question thought @ChmE. You substitute the first equation into the second one right

Answer 22

I did 2nd into first cuz there is already an x alone so it made it quicker

Answer 23

Yeah. Thanks, don't know how I missed it.

Answer 24

\[2x+3y=4\]\[x-2y=-5\]We need to get one of the variables with the same coefficient. So lets multiply the second equation by 2.\[2x-4y=-10\]Now that we have a 2x in both equations we can ELIMINATE that term by subtracting the equations old school. One on top of the other and subtract like terms.\[7y=14\]2x-2x=0, 3x-(-4x)=7x, 4-(-10)=14
Now we solve for y and get 2. Plugging it into the 2nd equation because it is simpler we get -1 for x

Answer 25

(3y**-(-4y**)=7y**)

Answer 26

2x + 3y = 4
x - 2y = (-5)
+2y +2y
x = -5 + 2y
2(-5 + 2y) + 3y = 4
-10 + 4y + 3y = 4
+10 +10
4y + 3y = 14
7y = 14
-- ---
7 7
y = 2

Answer 27

2x + 3y = 4
2x + 3(2) = 4
2x + 6 = 4
- 6 -6
2x = -2
-- ---
2 2
x = (-1)

Answer 28

So, the solution is (-1,2)
The value of x is (-1)

Answer 29

@ChmE, so is my answer correct?
I think so!

Answer 30

How would you get x by itself if there is a number in front of it, like lets say..
5x + 4y = 1 ?

Answer 31

You can't x by itself, so you would have to do this:

Answer 32

you can... x=(-4y+1)/5

Answer 33

5x + 4y = 1
-5x -5x
4y = 1 - 5x
And solve your problem using that equation!

Answer 34

@ChmE, is that right?

Answer 35

ya\[x=-\frac{ 4y }{ 5 }+\frac{ 1 }{ 5 }\]You are just solving for x even though there is another unknown. It is possible to get it by itself but not get a value. You always need the same amount of equations as unknowns to solve for a value.

Answer 36

Thanks, @ChmE. @alienababy needs help on another problem.
Are you going to help with it?

Answer 37

@Johnjakile1998 & @ChmE ; What is the value of the y variable in the solution to the following system of equations?
5x+4y=1
4x+3y=-1

Answer 38

Are you ready for this @ChmE?

Answer 39

I'm solving the problem @alienababy

Answer 40

thankyou @Johnjakile1998

Answer 41

Welcome! While, I'm solving this problem. I wanted to know if you needed help on another question?

Answer 42

Use the Substitution Method to solve the following system of equations.
2x + y = 3
-3x + 4y = 1

Answer 43

Which do I solve first?

Answer 44

the first one i gave you.

Answer 45

Cool. Come on @ChmE!

Answer 46

For the above question for which I was mentioned in. I would use the elimination method because both variables have a coefficient. It will begin to get messy by substitution illustrated by me solving for x just a couple lines earlier. I'm going to let you attempt it first. If you follow my instructions for this method in the beginning I'm confident you'll get the right answer.

Answer 47

@ChmE which one should i multiply first?

Answer 48

Thanks! That's why I'm so lost.

Answer 49

like in fractions find the lowest common multiple. In this case it is 12. The above equation needs to be multiplied by 3 and the bottom by 4. remember to multiple every term

Answer 50

@alienababy. I'm going to solve the second equation first! I already got the answer!

Answer 51

multiply**

Answer 52

okay :) @Johnjakile1998 & @ChmE i got 15x+12y=3 then 16x+12=-4. is that right?

Answer 53

For which problem?

Answer 54

mine

Answer 55

the first one, using the elimination method.

Answer 56

its correct now subtract old school

Answer 57

You're so weird @ChmE! Lol

Answer 58

i got -x+y=-1 ? that doesnt seem right to me.

Answer 59

@ChmE

Answer 60

you shouldn't get a y term try again

Answer 61

-x=-1 @ChmE

Answer 62

@alienababy. I got the answer for the second equation. Want me to post it?

Answer 63

yes please @Johnjakile1998

Answer 64

what is -4-3?

Answer 65

-7 @ChmE

Answer 66

-7.

Answer 67

x=-7

Answer 68

you can put whatever equation u want on top when subtracting. i put the 16x equation on top so that my x would be positive after subtraction.

Answer 69

eliminates possible stupid mistakes

Answer 70

oh.. @ChmE i didnt know that.

Answer 71

if you want to see it for yourself. do the subtraction both ways. you should get -x=7 and x=-7. those or equal, no?

Answer 72

yes, i did. @ChmE

Answer 73

are**. Nice

Answer 74

now just plug ur value of x into one of the equations, choosing the easier one (why make it even harder), and solve for y

Answer 75

the first equations, or the second equations after you solved it? @ChmE

Answer 76

whatever you want in this case. both equations look the same to me. It was more of a general statement

Answer 77

okay.

Answer 78

you want to use the original equations because it is simpler. smaller numbers

Answer 79

2x + y = 3
-2x -2x
y = 3 - 2x
-3x + 4(3 - 2x) = 1
-3x + 12 - 8x = 1
-11x + 12 = 1
- 12 -12
-11x = -11
x = 1
2x + y = 3
2(1) + y = 3
2 + y = 3
-2 -2
y = 1
So, the solution is (1,1)

Answer 80

gotcha. so it doesnt matter though? @ChmE

Answer 81

no. You should get the same answer in either case. I'd encourage you to try it to see for yourself.

Answer 82

thankyou @Johnjakile1998

Answer 83

So, @alienababy that's the answer for the second equation.
Is the answer right @ChmE?

Answer 84

Any other questions @alienababy

Answer 85

looks correct to me

Answer 86

can i just be a math genious ? ):

Answer 87

@ChmE i got -9?

Answer 88

thanks @ChmE! You are @alienababy, just Algebra 1 isn't the math that is you're strongest. For all we know your strongest math is Calculus or Alebra 2 even Geometry!

Answer 89

thanks :) @Johnjakile1998

Answer 90

any others questions @alienababy

Answer 91

Just wait.. Here's a problem I had on my last test\[y-\ln y=x ^{2}+1\]is this a solution of \[\frac{ dy }{ dx }=\frac{ 2xy }{ y-1 }?\]

Answer 92

What kinda math is this?

Answer 93

I got positive 9

Answer 94

Differential Equations (Calc 4)