Question

y – 3)/4 + (y – 1)/5 – (y – 2)/3 = 1
(3x – 2)/3 + (2x + 3)/3 = (x + 7)/6
(8y – 5)/(7y + 1) = -4/5
(5 – 7y)/(2 + 4y) = -8/7. Solve these linear equations.. pls answerrr fastt​

Answer 1

Answer:

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Answer 2

(i) x + y = 14 .....(i)

x – y = 4 ......(ii)

Let us consider the Equation (ii)

x – y = 4

x = 4 + y ......(iii)

Put the value of x = 4 + y in Equation (i), we get

4 + y + y = 14

2y = 14 - 4

2y = 10

y = 10/2

y = 5

Put the value of y = 5 in equation (i)

x + 5 = 14

x = 14 - 5

x = 9, y = 5

(ii) s – t = 3 .....(i)

s/3 + t/2 = 6

(2s + 3t)/6 = 6

2s + 3t = 36 ......(ii)

Let us consider the Equation (i)

s – t = 3

s = t + 3 ......(iii)

Put the value of s = t + 3 in Equation (ii), we get

2(t + 3) + 3t = 36

2t + 6 + 3t = 36

5t = 36 - 6

5t = 30

t = 30/5

t = 6

Put the value of t = 6 in equation (iii)

s = 6 + 3

s = 9, t = 6

x = 14 - 5

x = 9, y = 5

(iii) 3x – y = 3 .....(i)

9x – 3y = 9 ......(ii)

Let us consider the Equation (i)

3x – y = 3

y = 3x - 3 ......(iii)

Put the value of y = 3x - 3 in Equation (ii), we get

9x – 3(3x - 3) = 9

9x - 9x + 9 = 9

9 = 9

This is always true.

Therefore, possible solution is x = 1, y = 0.

(iv) 0.2x + 0.3y = 1.3

2x + 3y = 13 .....(i)

0.4x + 0.5y = 2.3

4x + 5y = 23 ......(ii)

Let us consider the Equation (ii)

4x + 5y = 23

x = (23 - 5y)/4 ......(iii)

Put the value of x = (23 - 5y)/4 in Equation (i), we get

2(23 - 5y)/4 + 3y = 13

(23 - 5y)/2 + 3y = 13

23 - 5y + 6y = 26

y = 26 - 23

y = 3

Put the value of y = 3 in equation (iii)

x = (23 - 5 x 3)/4

x = (23 - 15)/4

x = 8/4

x = 2

x = 2, y = 3

(v) √2x + √3y = 0 .....(i)

√3x - √8y = 0 ......(ii)

Let us consider the Equation (ii)

√3x - √8y = 0

x = √8y/√3 ......(iii)

Put the value of x = √8y/√3 in Equation (i), we get

√2 x √8y/√3 + √3y = 0

√16y + 3y = 0

y(√16 + 3) = 0

y = 0 , x = 0

(vi) 3x/2 - 5y/3 = -2 .....(i)

x/3 + y/2 = 13/6 ......(ii)

Let us consider the Equation (ii)

x/3 + y/2 = 13/6

x/3 = 13/6 - y/2

x = 3(13 - 3y)/6

x = (13 - 3y)/2 ......(iii)

Put the value of x = (13 - 3y)/2 in Equation (i), we get

4 + y + y = 14

2y = 14 - 4

2y = 10

y = 10/2

y = 5

Put the value of y = 5 in equation (i)

x + 5 = 14

x = 14 - 5

x = 9, y = 5

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