solve the following system of equations?

Question

5x=6y+40 and the bottom will be
2y=8-3x

Answer 1

5x=6y+40
2y=8-3x

Solve one equation for one of the variables...
5x = 6y + 40
x = (6/5)y + 8

now, put that into the unused equation...
2y = 8 - 3x
2y = 8 - 3(6/5 y + 8)
2y = 8 - (18/5)y - 24
2y = -(18/5) y - 16

Multiply everything by 5 to get rid of the fraction...
10y = -18y - 80
28y = - 80
y = -80/28 = -20 / 7

Now, put that back into one of the equations to find x.

x = (6/5)y + 8
x = (6/5)(-20/7) + 8
x = (6/1)(-4/7) + 8
x = (-24/7) + 56/7
x = 32/7

So, the answer is (32/7 , -20/7)

Answer 2

5x = 6y + 40- - - - - - -Equation 1
2y = 6 - 3x- - - - - - - - Equation 2
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Convert equation 1 and equation 2 to standard form

5x = 6y + 40

5x - 6y - 6y + 40 - 6y

5x - 6y = 40. . . . .Standard form equation 1

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2y = 8 - 3x

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

3x + 2y = 8. . . . . . .Standard form equation 2

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5x - 6y = 40
3x + 2y = 8
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Multiply standard form equation 2 by 3

3x + 2y = 8

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

9x + 6y = 24

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5x - 6y = 40
9x + 6y = 24
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14x = 64

14x / 14 = 64 / 14

x = 64/14

x = 32/7

Insert the x value into equation 2
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2y = 8 - 3x

2y = 8 - 3(32/7)

2y = 8 - 96/7

2y = 56/7 - 96/7

2y = - 40/7

2y / 2 = - 40/7 ÷ 2/1

y = - 40/7 x 1/2

y = - 40 / `14

y = - 20 / 7

Insert the y value into equation 2
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Check equation 2

2x = 8 - 3x

2(- 20/7) = 8 - 3(32/7)

- 40/7 = 8 - 96/7

- 40/7 = 56/7 - 96/7

- 40/7 = - 40/7

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Check equation 1

5x = 6y + 40

5(32/7) = 6(- 20/7) + 40

160/7 = - 120/7 + 280/7

160/7 = 160/7

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Both equations balance

The solution set is { 32/7, - 20/7 }

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Answer 3

Since 2y=9-3x, then 6y = 24-9x.
Substituting this in first equation gives 5x=24-9x+40 and
14x = 64, thus x= 32/7 then 2y= 8-96/7 and 2y= -40/7 and
y=-20/7

Answer 4

5x - 6y = 40
3x + 2y = 8--------X by 3

5x - 6y = 40
9x + 6y = 24-------ADD
14x = 64
x = 64 / 14 = 32 / 7

96/7 + 2y = 8
2y = 56/7 - 96/7
2y = - 40 / 7
y = - 20 / 7

x = 32 / 7 , y = - 20 / 7

Answer 5

i got as far as


-5/3x = 3y - 5

It should be taken down further