2 8 x + 4 7 y = 12 - 2 8 x + 4 7 y = 12 The

Question

2 8 x + 4 7 y = 12 - 2 8 x + 4 7 y = 12 The solution to the given system of equations is x , y . What is the value of 8 x + 7 y ?

Accepted Answer

The correct answer is 3 . Adding the second equation to the first equation in the given system of equations yields 2 8 x - 2 8 x + 4 7 y + 4 7 y = 12 + 12 , or 8 7 y = 24 . Dividing both sides of this equation by 8 yields 7 y = 3 . Substituting 3 for 7 y in the first equation, 2 8 x + 4 7 y = 12 , yields 2 8 x + 4 3 = 12 , or 2 8 x + 12 = 12 . Subtracting 12 from both sides of this equation yields 2 8 x = 0 . Dividing both sides of this equation by 2 yields 8 x = 0 . Substituting 0 for 8 x and 3 for 7 y in the expression 8 x + 7 y yields 0 + 3 , or 3 . Therefore, the value of 8 x + 7 y is 3 .

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