Question

Solve by Substitution

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−5r + 5s + 3t = −23

−5r + 3s − 3t = −11

−6r + 6t = −12

Answer 1

Solution:

The given equations are

- 5r + 5s + 3t = - 23 ..... (i)

- 5r + 3s - 3t = - 11 ..... (ii)

- 6r + 6t = - 12 ..... (iii)

From (iii), we gey

- r + t = - 2

or, t = r - 2

Putting t = r - 2 from (i), we get

- 5r + 5s + 3 (r - 2) = - 23

or, - 5r + 5s + 3r - 6 = - 23

or, - 2r + 5s = - 17 ..... (iv)

Again, putting t = r - 2 from (ii), we get

- 5r + 3s - 3 (r - 2) = - 12

or, - 5r + 3s - 3r + 6 = - 12

or, - 8r + 3s = - 18 ..... (v)

Multiplying (iv) by 4 and subtracting from (v), we get

- 8r + 3s + 8r - 40s = - 18 + 68

or, - 37s = 50

or, s = - 50/37

From (iv), putting s = - 50/37, we get

- 2r + 5 (- 50/37) = - 17

or, - 2r - 250/37 = - 17

or, 2r = 17 - 250/37

or, 2r = (629 - 250)/37

or, 2r = 379/37

or, r = 379/74

From (iii), we get

t = 379/74 - 2

or, t = (379 - 148)/74

or, t = 231/74

Therefore, the required solution is

r = 379/74, s = - 50/37, t = 231/74