Write as a Vector Equality (3x)/2-y=3 , x-(4y)/3=4

Problem

{[(3*x)/2−y=3],[x−(4*y)/3=4])

Solution

1. Identify the coefficients of the variables x and y in each equation to form the column vectors.

2. Extract the x coefficients from the left side of the system to create the first vector: ([3/2],[1])

3. Extract the y coefficients from the left side of the system to create the second vector: ([−1],[−4/3])

4. Identify the constants on the right side of the equations to form the constant vector: ([3],[4])

5. Combine these components into a single vector equation where the variables x and y scale their respective coefficient vectors.

Final Answer

x*([3/2],[1])+y*([−1],[−4/3])=([3],[4])

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