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Question

# Question 1 (iii) Solve the following pair of linear equations 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) And we have 9x−2y=7...(ii) Subtracting equation (ii) from equation (iii), we get -13y = 5 y=−513 Putting value in equation (i), we get 3x - 5y = 4 ... (i) 3x−5(−513)=4 Multiplying by 13, we get 39x + 25 = 52 39x = 27 x=2739=913 Therefore, x=913 and y=−513 By substitution method: 3x – 5y = 4 ... (i) Adding 5y on both sides, we get 3x = 4 + 5y Dividing by 3, we get, x=4+5y3 ... (iv) Putting this value in equation (ii) we get, 9x - 2y = 7 ... (ii) ⇒9(4+5y)3−2y=7 ⇒3(4+5y)−2y=7 ⇒12+15y−2y=7 ⇒13y=−5 ⇒y=−513 Substituting the value in equation (iv), we obtain: x=4+5×−5133 ⇒x=913 ∴x=913,y=−513 Hence, we get x=913 and y=−513

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