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Question
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
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Solution
3x – 5y – 4 = 0 and 9x = 2y + 7
By elimination method
3x – 5y – 4 = 0
3x – 5y = 4 ...(i)
9x = 2y + 7
9x – 2y = 7 ...(ii)
Multiplying equation (i) by 3, we get
9x – 15y = 12 ...(iii)
9x – 2y = 7 ...(ii)
Subtracting equation (ii) from equation (iii), we get
-13y = -5
y = `-5/13`
Putting value in equation (i), we get
3x – 5y = 4 ...(i)
`3x - 5(-5/13) = 4`
Multiplying by 13 we get
39x + 25 = 52
39x = 27
x = `27/39`
x = `9/13`
Hence, our answer is `x = 9/13 and y = - 5/13`
By substitution method
3x - 5y- 4 = 0
9x - 2y - 7 = 0
`y = (3x - 4)/5`
Putting `y = (3x - 4)/5-7 = 0`
45x - 6x + 8 - 35 = 0
39x = 27
x = `27/39`
x = `9/13`
Putting x = `9/13`
y = `(3xx9/13 - 4)/5`
y = `(27 - 52)/65`
y = `-25 /65`
y = `-5/13`
Hence, x = `9/13` and y = `-5/13`
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