Write as a Vector Equality y-5=x , y-7=2x

Problem

{[y−5=x],[y−7=2*x])

Solution

1. Rearrange the equations into standard form a*x+b*y=c by moving the variables to one side and constants to the other.

x−y=−5

2*x−y=−7

2. Identify the coefficients of x and y to form the coefficient matrix and the constants to form the result vector.

Coefficients of *x:([1],[2])

Coefficients of *y:([−1],[−1])

Constants:([−5],[−7])

3. Express the system as a linear combination of vectors by multiplying the variable scalars by their respective coefficient columns.

x*([1],[2])+y*([−1],[−1])=([−5],[−7])

Final Answer

x*([1],[2])+y*([−1],[−1])=([−5],[−7])

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