Write as a Vector Equality x^2-y^2=84 , x+y=16

Problem

x2−y2=84,x+y=16

Solution

1. Factor the first equation using the difference of squares identity, which states that a2−b2=(a−b)*(a+b)

(x−y)*(x+y)=84

2. Substitute the value from the second equation, x+y=16 into the factored form of the first equation.

(x−y)*(16)=84

3. Solve for the term (x−y) by dividing both sides by 16

x−y=84/16

4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 4

x−y=21/4

5. Express the system of linear equations as a single vector equality where the left side is a vector of the expressions and the right side is a vector of the constants.

([x+y],[x−y])=([16],[21/4])

Final Answer

([x+y],[x−y])=([16],[5.25])

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