Write as a Vector Equality 5x-2y=12 , x=3y+5

Problem

{[5*x−2*y=12],[x=3*y+5])

Solution

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

x−3*y=5

2. Write the system of linear equations as a single vector equation by grouping the coefficients of x and y into column vectors.

x*[[5],[1]]+y*[[−2],[−3]]=[[12],[5]]

3. Express the system in matrix-vector form A*x=b by placing the coefficients into a 2×2 matrix.

[[5,−2],[1,−3]]*[[x],[y]]=[[12],[5]]

Final Answer

[[5,−2],[1,−3]]*[[x],[y]]=[[12],[5]]

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