Simeltaneous Equasions...?

Question

How do i do them, whats a good way ?

Heres one...

2x+3y=1
3x-2y=8

Answer 1

people like me without brains cannot answers this stuff

Answer 2

Elimination by addition method

2x + 3y = 1- - - - - - -equation 1
3x - 2y = 8- - - - - - - -Equation 2
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Multiply equation 1 by 2 and equation 2 by 3

2x + 3y = 1

2(2x) + 2(3y) = 2(1)

4x + 6y = 2

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3x - 3y = 8

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

9x - 6y = 24

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Elimination of y

4x + 6y = 2
9x - 6y = 24
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13x = 26

13x / 13 = 26 / 13

x = 26 / 13

x = 2

insert the x value into equation 1

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2x + 3y = 1

2(2) + 3y = 1

4 + 3y = 1

4 + 3y - 4 = 1 - 4

3y = - 3

3y / 3 = - 3 /3

y = - 3/3

y = - 1

Insert the y value into equation 1

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Check for equation 1

2x + 3y = 1

2(2) + 3(- 1) = 1

4 + (- 3) = 1

4 - 3 = 1

1 = 1

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Check for equation 2

3x - 2y = 8

3(2) - 2(- 1) = 8

6 - (- 2) = 8

6 + 2 = 8

8 = 8

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Both equations balance

The solution set is { 2, - 1 }

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Answer 3

Elimination by addition

Add the first equation and the second equation
2x + 3y = 1 (Equation 1)
+ 3x - 2y = 8 (Equation 2)
____________
5x + y = 9
y = 9 - 5x (Equation 3)

Substitute Equation 3 to either Eq. 1 or 2

3x - 2y = 8 (Eq. 2)
3x - 2(9 -5x) = 8
3x - 18 + 10x = 8
13x - 18 = 8
13x - 18 + 18 = 8 + 18
x = 26/13
x = 2 ====> value of x
Substitute the valeu of x to Equation 1
2x + 3y = 1 (Eq. 1)
2(2) + 3y = 1
4 + 3y = 1
3y = 1-4
3y = - 3
y = -3/3
y = -1 ====> value of y

Answer 4

Just substitute the value of X from the 1st equ to the 2nd

X=2
Y= - 1

Answer 5

elimination works best for me!

(2x+3y=1)*2 4x+6y=2
(3x-2y=8)*3 9x-6y=24
13x=26
x=2
2x+3y=1 (substitute x)
3y=(-3)
y=(-1)