Write as a Vector Equality 2x-y=10 , x=1/2y+5

Problem

2*x−y=10,x=1/2*y+5

Solution

1. Identify the system of linear equations. The given equations are 2*x−y=10 and x=1/2*y+5

2. Rearrange the second equation into standard form a*x+b*y=c to align the variables. Subtracting 1/2*y from both sides of x=1/2*y+5 gives x−1/2*y=5

3. Observe that the two equations are dependent. Multiplying x−1/2*y=5 by 2 results in 2*x−y=10 which is identical to the first equation.

4. Express the system using vector notation. A system of linear equations can be written as a linear combination of column vectors where the variables x and y act as scalars.

5. Formulate the vector equality by separating the coefficients of x and y into distinct vectors and setting them equal to the constant vector.

Final Answer

x*[[2],[1]]+y*[[−1],[−1/2]]=[[10],[5]]

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