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1/2x +1/3y = 7
1/4x +2/3 y = 6

What is the solution of the system shown?

(1/6 , 14)
(6, 12)
(10 2/3 , 5)

Respuesta :

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The answer is 10 2/3, 5

Proof:

Solve the following system:
{x/2 + y/3 = 7 | (equation 1)
{x/4 + (2 y)/3 = 6 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:
{x/2 + y/3 = 7 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)

Multiply equation 1 by 6:
{3 x + 2 y = 42 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)

Multiply equation 2 by 2:
{3 x + 2 y = 42 | (equation 1)
{0 x+y = 5 | (equation 2)

Subtract 2 × (equation 2) from equation 1:
{3 x+0 y = 32 | (equation 1)
{0 x+y = 5 | (equation 2)

Divide equation 1 by 3:
{x+0 y = 32/3 | (equation 1)
{0 x+y = 5 | (equation 2)
Collect results:
Answer: {x = 10 2/3, y = 5

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