# what is the solution of the system of equations ?  6x + 12y = -6 3x - 2y = -27?

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• what is the solution of the system of equations ?  x + 2y = -1 and 3x - 2y = -27?

-1×-2 - 2×-27 = 56, 1×-27 - -1×3 = -24,  and 1×-2 - 2×3 = -8

Solution: x = 56/8 = 7 and y = -24/8 = -3

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The intersection of ax+by=c and dx+ey=f is ((c×e-b×f)/(a×e-b×d), (a×f-c×d)/(a×e-b×d)) where the lines are not parallel.

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• 6x+12y=-6

3x-2y=-27

=>

x=-7

y=3

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• This is a simultaneous equation:

(i) 6x + 12y = -6

(ii) 3x - 2y = -27

You need to eliminate one variable. Multiply (ii) by 2

(iii) 6x - 4y = - 54

and subtract the answer from (i)

(iv) 16y = 48

(v) y = 3

Substitute into any of the equations (iii) is simplest:

(vi) 6x - (4 x 3) = -54

6x - 12 = -54

6x = -42

(vii) x = -7

ANS x = -7, y = 3

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• 6x + 12y = -6,eq1   3x - 2y = -27 eq2

6x + 12y = - 6

6[3x - 2y = - 27]... multiply equation 2 by 6

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6x + 12y = - 6

18x - 12y = - 162

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...24x = -168

plug in x = - 7 to equation 1

6x + 12y = - 6

6(-7) + 12y = - 6

- 42 + 12y = - 6

12y = - 6 + 42

12y = 36

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• 6x+12y=-6;       3x-2y=-27 (*2)

6x-4y=-54 (subtract)

16y=48 >>y=3

6x+36=-6

6x=-42

x=-7

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• 6x + 12y = -6

3x - 2y = -27

3x + 6y = -3

8y = 24

y = 3

x = -7

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• 6x + 12y = -6

3x - 2y = -27

3x + 6y = -3

8y = 24

y = 3

x = -7

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• Solve Simultaneously

6x + 12y = -6

3x - 2y = -27

Multiply the bottom eq'n by '-2' and then add the two eq'ns , this will eliminate 'x'

Hence

6x + 12y = -6

-6x + 4y = 54

16y = 48

y = 3

When y = 3 substitute into either eq'n for 'x'

6x + 12(3) = -6

6x + 36 = -3

6x = -39

x = -6 1/2 or -6.5

Hence in (x,y) form the answer is ( -6.5 , 3)

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• Is this q your studies. I will suggest you to go and solve it by yourself ONLY.

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• 6x + 12y = -6 … 

3x - 2y = -27 … 

 ÷ 6:

x + 2y = -1 … 

 + :

3x + x = -27 + (-1)

4x = -28

x = -7

Plug x = -7 into :

-7 + 2y = -1

2y = 6

x = 3

Hence, (x, y) = (3, -7)

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