Question

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Answer 1

• k = - 7/3

Explanation:

The given expression is the sum of three non-negative expressions. The square is zero or positive, the absolute value is zero or positive.

Since the sum is zero, each of the expressions should equal zero:

• 2x + 5y - 7 = 0
• 4x - 2y = 0
• 5x - 1/2y + k = 0

From the first 2 equations we get:

• 4x = 2y ⇒ y = 2x
• 2x + 5(2x) = 7
• 12x = 7
• x = 7/12

Find the value of y:

• y = 2x= 2*7/12 = 7/6

Substitute the values into third equation and find the value of k:

• 5x - 1/2y + k = 0
• 5*7/12 - 1/2(7/6) + k = 0
• 35/12 - 7/12 = - k
• 28/12 = - k
• 7/3 = - k
• k = - 7/3