Write as a Vector Equality y=1/2x-3 , 2x+y=2

Problem

y=1/2*x−3,2*x+y=2

Solution

1. Rearrange the first equation into standard form A*x+B*y=C by multiplying by 2 and moving the x term to the left.

2*y=x−6

−x+2*y=−6

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

A=([−1,2],[2,1])

3. Define the vector of variables v and the vector of constants b

v=([x],[y])

b=([−6],[2])

4. Construct the vector equality by expressing the system in the form A*v=b

([−1,2],[2,1])*([x],[y])=([−6],[2])

Final Answer

([−1,2],[2,1])*([x],[y])=([−6],[2])

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