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3. Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9 3x + 2y = 4

3. Solve the following pair of linear equations by the substitution and cross-multiplication methods:

8x + 5y = 9

3x + 2y = 4

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Solution: 8x + 5y = 9 …………………..(1) 3x + 2y = 4 ……………….….(2) From equation (2) we get x = (4 – 2y )/ 3 ……………………. (3) Using this value in equation 1, we get 8(4-2y)/3 + 5y = 9 32 – 16y +15y = 27 -y = -5 y = 5 ……………………………….(4) Using this value in equation (2), we get 3x + 10 = 4 x = -2 Thus, x = -2 and y = 5. Now, Using Cross Multiplication method: 8x +5y – 9 = 0 3x + 2y – 4 = 0 x/(-20+18) = y/(-27 + 32 ) = 1/(16-15) -x/2 = y/5 =1/1 ∴ x = -2 and y =5.

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