Write as a Vector Equality 3x-2y=8 , 6y=15x+12

Problem

{[3*x−2*y=8],[6*y=15*x+12])

Solution

1. Rearrange the equations into standard form a*x+b*y=c so that the variables x and y are aligned on the left side.

3*x−2*y=8

−15*x+6*y=12

2. Identify the coefficients of x and y to form the column vectors for each variable.

Coefficients of *x:[[3],[−15]]

Coefficients of *y:[[−2],[6]]

3. Identify the constants on the right side to form the constant vector.

Constants:[[8],[12]]

4. Construct the vector equation by multiplying each variable by its corresponding coefficient vector and setting their sum equal to the constant vector.

x*[[3],[−15]]+y*[[−2],[6]]=[[8],[12]]

Final Answer

x*[[3],[−15]]+y*[[−2],[6]]=[[8],[12]]

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