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

Problem

{[y=3*x+5],[5*x−4*y=−3])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting 3*x from both sides.

−3*x+y=5

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

−3*x+1*y=5

5*x−4*y=−3

3. Separate the coefficients of x and y into distinct column vectors.

x*[[−3],[5]]+y*[[1],[−4]]=[[5],[−3]]

4. Rewrite the system as a single matrix-vector product A*x=b

[[−3,1],[5,−4]]*[[x],[y]]=[[5],[−3]]

Final Answer

[[−3,1],[5,−4]]*[[x],[y]]=[[5],[−3]]

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