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

Problem

2*x+y=3,y=2*x−3

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.

2*x+y=3

−2*x+y=−3

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

Coefficients of *x:([2],[−2])

Coefficients of *y:([1],[1])

3. Express the system as a linear combination of these column vectors equated to the constant vector.

x*([2],[−2])+y*([1],[1])=([3],[−3])

4. Rewrite the linear combination as a single vector equality by performing scalar multiplication and vector addition.

([2*x+y],[−2*x+y])=([3],[−3])

Final Answer

([2*x+y],[−2*x+y])=([3],[−3])

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