Write as a Vector Equality 50x+32y=3500 , 50x+32(0)=350

Problem

50*x+32*y=3500,50*x+32*(0)=350

Solution

1. Identify the coefficients and variables in the first equation to form a dot product.

2. Represent the left side of the equation 50*x+32*y as the dot product of a coefficient vector and a variable vector.

3. Define the coefficient vector as ([50],[32]) and the variable vector as ([x],[y])

4. Express the first equation as a vector equality.

([50],[32])⋅([x],[y])=3500

5. Express the second equation 50*x+32*(0)=350 using the same vector structure, substituting 0 for y

([50],[32])⋅([x],[0])=350

Final Answer

([50],[32])⋅([x],[y])=3500,([50],[32])⋅([x],[0])=350

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