Question

Solve simultaneous equation please 3s²+2t²=11; 3s+2t=1

Answer 1

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Step-by-step explanation:

3s² + 2t² = 11-----------------------(1)

3s + 2t = 1 --------------------------(2)

From (2)

3s = 1 - 2t

s = (1 - 2t) / 3----------------------(3)

Substitute (3) into (1)

3s² + 2t² = 11

3[ (1 - 2t) / 3 ] ² + 2t² = 11

3 [ (1 - 2t)² / 9 ] + 2t² - 11 = 0

(1 - 2t)² / 3 + 2t² - 11 = 0

Multiply the equation with 3,

(1 - 2t)² + 6t² - 33 = 0

1 - 4t + 4t² + 6t² - 33 = 0

10t² - 4t - 32 = 0

5t² - 2t - 16 = 0

Factorize the equation,

(5t + 8) (t - 2) = 0

(5t + 8) = 0            

t = -8/5  

OR

(t - 2) = 0

t = 2

Substitute values of t into (2)

3s + 2t = 1

3s + 2(-8/5) = 1

3s = 1 + 16/5

s = 7/5

OR

3s + 2(2) = 1

3s = 1 - 4

s = -1

Therefore,

t = -8/5, s = 7/5

t = 2, s = -1