Write as a Vector Equality x+4y=6 , 3x+12y=18

Problem

{[x+4*y=6],[3*x+12*y=18])

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 to create the first vector: ([1],[3])

3. Extract the y coefficients from the left side to create the second vector: ([4],[12])

4. Identify the constants on the right side of the equations to form the resultant vector: ([6],[18])

5. Combine these into a linear combination where the variables x and y scale their respective coefficient vectors.

Final Answer

x*([1],[3])+y*([4],[12])=([6],[18])

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