Write as a Vector Equality y=3x+6 , 4x-5y=-19

Problem

{[y=3*x+6],[4*x−5*y=−19])

Solution

1. Rearrange the first equation into standard form A*x+B*y=C by subtracting 3*x from both sides.

−3*x+y=6

2. Align the system of linear equations to prepare for vector notation.

−3*x+1*y=6

4*x−5*y=−19

3. Identify the coefficients of x and y to form the column vectors.

Coefficients of *x:([−3],[4])

Coefficients of *y:([1],[−5])

4. Construct the vector equation by multiplying each variable by its corresponding coefficient vector and setting the sum equal to the constant vector.

x*([−3],[4])+y*([1],[−5])=([6],[−19])

Final Answer

x*([−3],[4])+y*([1],[−5])=([6],[−19])

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