Write as a Vector Equality x=-3y , 7x-2y=-69

Problem

{[x=−3*y],[7*x−2*y=−69])

Solution

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

x+3*y=0

2. Identify the coefficients of x and y from both equations to form the vectors on the left side.

{[1*x+3*y=0],[7*x−2*y=−69])

3. Express the system as a linear combination of two column vectors, one scaled by x and the other scaled by y

x*[[1],[7]]+y*[[3],[−2]]=[[0],[−69]]

Final Answer

x*[[1],[7]]+y*[[3],[−2]]=[[0],[−69]]

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