Write as a Vector Equality (4x-y)=6 , (1/2y)=-3+2x

Problem

{[4*x−y=6],[1/2*y=−3+2*x])

Solution

1. Rearrange the second equation into standard form a*x+b*y=c by moving the x term to the left side.

−2*x+1/2*y=−3

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

A=([4,−1],[−2,1/2])

3. Define the variable vector x and the constant vector b from the right-hand side values.

x=([x],[y])

b=([6],[−3])

4. Construct the vector equality by expressing the system in the form A*x=b or as a linear combination of column vectors.

x*([4],[−2])+y*([−1],[1/2])=([6],[−3])

Final Answer

([4,−1],[−2,1/2])*([x],[y])=([6],[−3])

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