Write as a Vector Equality y=-x , 3x-5y=15

Problem

y=−x,3*x−5*y=15

Solution

1. Identify the system of linear equations in standard form a*x+b*y=c

y=−x⇒x+y=0

3*x−5*y=15

2. Express the system as a single vector equation by separating the coefficients of x and y into column vectors.

x*[[1],[3]]+y*[[1],[−5]]=[[0],[15]]

3. Rewrite the equation in the standard matrix-vector form A*x=b where A is the coefficient matrix.

[[1,1],[3,−5]]*[[x],[y]]=[[0],[15]]

Final Answer

[[1,1],[3,−5]]*[[x],[y]]=[[0],[15]]

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