Write as a Vector Equality y=2x-3 , 5x-y=13.5

Problem

{[y=2*x−3],[5*x−y=13.5])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 2*x from both sides.

−2*x+y=−3

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

([−2,1],[5,−1])

3. Define the variable vector and the constant vector based on the right-hand sides of the equations.

v=([x],[y])

b=([−3],[13.5])

4. Express the system as a linear combination of vectors by separating the x and y components.

x*([−2],[5])+y*([1],[−1])=([−3],[13.5])

Final Answer

x*([−2],[5])+y*([1],[−1])=([−3],[13.5])

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