Write as a Vector Equality (3x-2y)=7 , (y)=2x-1

Problem

{[3*x−2*y=7],[y=2*x−1])

Solution

1. Rearrange the second equation into standard form a*x+b*y=c by subtracting 2*x from both sides.

−2*x+y=−1

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

([3,−2],[−2,1])

3. Define the variable vector and the constant vector from the right-hand sides of the equations.

x=([x],[y])

b=([7],[−1])

4. Express the system as a linear combination of column vectors by multiplying the variables by their respective coefficient columns.

x*([3],[−2])+y*([−2],[1])=([7],[−1])

Final Answer

x*([3],[−2])+y*([−2],[1])=([7],[−1])

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