Write as a Vector Equality 2x=3y-4 , -6x+12y=26

Problem

{[2*x=3*y−4],[−6*x+12*y=26])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 3*y from both sides.

2*x−3*y=−4

2. Identify the coefficients of x and y from both equations to form the coefficient matrix and the constant terms to form the constant vector.

Equation 1: *2*x−3*y=−4

Equation 2: −6*x+12*y=26

3. Express the system as a linear combination of two column vectors, where the scalars are the variables x and y

x*[[2],[−6]]+y*[[−3],[12]]=[[−4],[26]]

Final Answer

x*[[2],[−6]]+y*[[−3],[12]]=[[−4],[26]]

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