Solve by the elimination method.?

Question

1/3x + 2/1y = 2/1

2/3x - 3/5y = 2/5

What is the solution of the system?

Answer 1

1/3x +2y = 2

2/3x -3/5y = 2/5

Multiply the second equation by 1/2 =

1/3x - 3/10y = 1/5

Subtract it from the first
23/10y = 9/5

multiply by 10/23 on both sides

y= 18/23

From the first equation,

1/3x + 36/23 = 2

1/3x = 10/23

x = 30/23

Answer 2

1/3x + 2/1y= 2/1- - - - - - -Equation 1
2/3x - 3/5y = 2/5- - - - - - - Equation 2
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Convert equation 1 and 2 to standard form. Multiply equation 1 by 3 and equation 2 by 15

1/3x + 2/1y = 2/1

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

x + 6y = 6. . . .Standard form equation 1

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2/3x - 3/5y = 2/5

15(2/3x) = 15(3/4y) = 15(2/5)

10x - 9y = 6. . . Standard form equation 2

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x + 6y = 6
10x - 9x = 6
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Multiply standard form equatio 1 by 9 and stndard form equation 2 by 6

x + 6y = 6

9(x) + 9(6y) = 9)6)

9x + 54y = 64

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10x - 9y = 6

6((10x) - 6(9y) = 6(6)

60x - 54y = 36

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9x + 55y = 54
60x - 54 = 36
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69x = 90

69x / 69 = 90 / 69

x = 90 / 69

x = 30/23

Insert the x value into equation 2

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2/3x - 3/5y = 2/5

2/3(30/23) - 3/5y = 2/5

60 / 69 - 3/5y = 2/5

20 /23 - 3/5y = 2/5

20/23 - 3/5y - 20/23 = 2/5 - 20/23

- 3/5y = 2/5 - 20/23

- 3/5y = 46/115 - 100/115

- 3/5y = - 54/115

- 3/5y / - 3/5 = - 54/115 ÷ - 3/5

y = - 54/115 ÷ - 3/5

y = - 54/115 x 5/3

y = 18/23 x 1/1

y = 18/ 23

Insert the y value into equation 2

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Check for equation 2

2/3x - 3/5y = 2/5

2/3(30/23) - 3/5(18/23) = 2/5

60/69 - 54/ 115 = 2/5

20/23 - 54/225 = 2/5

100/115 - 54/115 = 2/5

46/115 = 2/5

2/5 = 2/5

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Check for equation 1

1/3x + 2/1y = 2/1

1/3(30/23) + 2/1(18/23) 2/1

30/69 + 36/23 = 2/1

10/23 + 36/23 = 2/1

46/23 = 2/1

2/1 = 2/1

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Both equations balance

The solution set is { 30/23, 18/23 }

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