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# Solve the following pair of linear equations by the elimination method and the substitution method:(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7 Q.1(3)

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The best two method of elimination and substitution how can i solve this question. Because it is very important type of question of class 10th math Solve the following pair of linear equations by the elimination method and the substitution method:(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7

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1. By the method of elimination:

3x – 5y – 4 = 0 ………………………………… (i)

9x = 2y + 7

9x – 2y – 7 = 0 …………………………………(ii)

When the equation (i) is multiplied by 3 we get,

9x – 15y – 12 = 0 ………………………………(iii)

When the equation (iii) is subtracted from equation (ii) we get,

13y = -5

y = -5/13 ………………………………………….(iv)

When equation (iv) is substituted in equation (i) we get,

3x +25/13 −4=0

3x = 27/13

x =9/13

∴x = 9/13 and y = -5/13

By the method of Substitution:

From the equation (i) we get,

x = (5y+4)/3 …………………………………………… (v)

Putting the value (v) in equation (ii) we get,

9(5y+4)/3 −2y −7=0

13y = -5

y = -5/13

Substituting this value in equation (v) we get,

x = (5(-5/13)+4)/3

x = 9/13

∴x = 9/13, y = -5/13

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